Physics

Internal v External

. The internal circuit is the part of the circuit where energy is being supplied to the charge. For the simple battery-powered circuit that we have been referring to, the portion of the circuit containing the electrochemical cells is the internal circuit. The external circuit is the part of the circuit where charge is moving outside the cells through the wires on its path from the high potential terminal to the low potential terminal. The movement of charge through the internal circuit requires energy since it is an uphill movement in a direction that is against the electric field. The movement of charge through the external circuit is natural since it is a movement in the direction of the electric field. When at the positive terminal of an electrochemical cell, a positive test charge is at a high electric pressure in the same manner that water at a water park is at a high water pressure after being pumped to the top of a water slide. Being under high electric pressure, a positive test charge spontaneously and naturally moves through the external circuit to the low pressure, low potential location.

Units of EPD

.Because electric potential difference is expressed in units of volts, it is sometimes referred to as the voltage.

For parallel circuits, the mathematical formula for computing the equivalent resistance (Req) is

1/Req= 1/R1+1/R2+1/R3.. where R1, R2, and R3 are the resistance values of the individual resistors that are connected in parallel

. Based on the information stated in the above question, explain the risk involved in using 14-gauge wire in a circuit that will be used to power an 16-ampere power saw.

A 12-gauge wire is wider than 14-gauge wire and thus has less resistance. The lesser resistance of 12-gauge wire means that it can allow charge to flow through it at a greater rate - that is, allow a larger current. Thus, 12-gauge wire can safely support a circuit that uses an appliance drawing up to 20 Amps of current. In fact, a 20-Amp circuit is protected by a fuse or circuit breaker that will flip off when the current reaches 20 Amps. If a 14-gauge wire was used on the same circuit, then the breaker would allow up to 20 Amps to flow through it. It could overheat and thus lead to the risk of fire. A 20-Amp circuit should never be wired using 14-gauge wire.

Household circuits are often wired with two different widths of wires: 12-gauge and 14-gauge. The 12-gauge wire has a diameter of 1/12 inch while the 14-gauge wire has a diameter of 1/14 inch. Thus, 12-gauge wire has a wider cross section than 14-gauge wire. A 20-Amp circuit used for wall receptacles should be wired using 12-gauge wire and a 15-Amp circuit used for lighting and fan circuits should be wired using 14-gauge wire. Explain the physics behind such an electrical code.

A 12-gauge wire is wider than 14-gauge wire and thus has less resistance. The lesser resistance of 12-gauge wire means that it can allow charge to flow through it at a greater rate - that is, allow a larger current. Thus, 12-gauge wire is used in circuits which are protected by 20-Amp fuses and circuit breakers. On the other hand, the thinner 14-gauge wire can support less current owing to its larger resistance; it is used in circuits which are protected by 15-Amp fuses and circuit breakers.

Symbols

A single cell or other power source is represented by a long and a short parallel line. A collection of cells or battery is represented by a collection of long and short parallel lines. In both cases, the long line is representative of the positive terminal of the energy source and the short line represents the negative terminal. A straight line is used to represent a connecting wire between any two components of the circuit. An electrical device that offers resistance to the flow of charge is generically referred to as a resistor and is represented by a zigzag line. An open switch is generally represented by providing a break in a straight line by lifting a portion of the line upward at a diagonal. These circuit symbols will be frequently used throughout the remainder of Lesson 4 as electric circuits are represented by schematic diagrams. It will be important to either memorize these symbols or to refer to this short listing frequently until you become accustomed to their use.

Third Variable Affecting Electrical Resistance

A third variable that is known to affect the resistance to charge flow is the material that a wire is made of. Not all materials are created equal in terms of their conductive ability. Some materials are better conductors than others and offer less resistance to the flow of charge. Silver is one of the best conductors but is never used in wires of household circuits due to its cost. Copper and aluminum are among the least expensive materials with suitable conducting ability to permit their use in wires of household circuits. The conducting ability of a material is often indicated by its resistivity. The resistivity of a material is dependent upon the material's electronic structure and its temperature. For most (but not all) materials, resistivity increases with increasing temperature. The table below lists resistivity values for various materials at temperatures of 20 degrees Celsius.

Analogy

A tollbooth is the main location of resistance to car flow on a tollway. Adding additional tollbooths within their own branch on a tollway will provide more pathways for cars to flow through the toll station. These additional tollbooths will decrease the overall resistance to car flow and increase the rate at which they flow.

If an electric circuit could be compared to a water circuit at a water park, then the current would be analogous to the?

A. water pressure B. gallons of water flowing down slide per minute C. water D. bottom of the slide E. water pump F. top of the slide Answer=B Reasoning=Current is the rate at which something flows. Electric current is the rate at which electric charge flows past a point on the electric circuit. Water current is the rate at which water flows past a point on the water circuit. As such, current is analogous to the number of gallons of water flowing into, along, and out of a slide per unit of time.

Ampere

Ampere is often shortened to Amp and is abbreviated by the unit symbol A.

. Determine the resistance of a 1-mile length of 12-gauge copper wire. Given: 1 mile = 1609 meters and diameter = 0.2117 cm.

Answer: 7.8 ohms Use the equation where L = 1609 m, A = PI•R2 (in meters2), and = 1.7 x 10-8 ohm•meter. First find the cross-sectional area: A = PI•R2 = (PI) • [ (0.002117 m) / 2)]2 = 3.519 x 10-6 m2 Now substitute into the above equation to determine the resistance. R = (1.7 x 10-8 ohm •m) • (1609 m) / (3.519 x 10-6 m2) R = 7.8 (7.7709 ohm)

A 12-V battery , a 12-ohm resistor and a 4-ohm resistor are connected as shown. The current in the 12-ohm resistor is ____ that in the 4-ohm resistor a. 1/3 b. 1/2 c. 2/3 d. the same as e. 1.5 times f. twice g. three times h. four times

Answer: A Reasoning=In parallel circuits, the electric potential difference across each resistor (ΔV) is the same. The current in a resistor follows Ohm's law: I = ΔV / R. Since the ΔV is the same for each resistor, the current will be smallest where the resistance is greatest. In fact, a resistor with three times the resistance will have one-third the current in order for the product of I•R to be the same. In this circuit, each resistor has a ΔV of 12 Volts. The 12-ohm resistor would have a current of 1 Amp (using Ohm's law equation) and the 4-ohm resistor would have a current of 3 Amps (using Ohm's law equation).

. Three identical light bulbs are connected to a D-cell as shown below. P, Q, X, Y and Z represent locations along the circuit. Which one of the following statements is true? a. The current at Y is greater than the current at Q. b. The current at Y is greater than the current at P. c. The current at Y is greater than the current at Z. d. The current at P is greater than the current at Q. e. The current at Q is greater than the current at P. f. The current is the same at all locations.

Answer: D Reasoning=Points P and X are outside the branches; they are at locations before (P) and after (X) the nodes. The current at these two locations are the same. The current at these locations are greater than the current at the other three locations since points P and X represent locations through which every charge must flow. Point Q comes after the node and at a location where charge to the middle and the right branch will flow. The current at this location is the greater than the current at locations Y and Z. Locations Y and Z represent locations where charge through a single branch will flow. The current at Y and Z is equal, but less than that at P.

Two wires - A and B - with circular cross-sections have identical lengths and are made of the same material. Yet, wire A has four times the resistance of wire B. How many times greater is the diameter of wire B than wire A?

Answer: DB = 2 • DA If wire A has four times the resistance, then it must have the smaller cross-sectional area since resistance and cross-sectional area are inversely proportional. In fact, A must have one-fourth the cross-sectional area of B. Since the cross-sectional area of a circular cross-section is given by the expression PI•R2, wire A must have one-half the radius of wire B and therefore one-half the diameter. Put another way, the diameter of wire B is two times greater than the diameter of wire A.

Three resistors are connected in parallel. If placed in a circuit with a 12-volt power supply. Determine the equivalent resistance, the total circuit current, and the voltage drop across and current in each resistor.

Answer=The analysis begins by using the resistance values for the individual resistors in order to determine the equivalent resistance of the circuit. 1 / Req = 1 / R1 + 1 / R2 + 1 / R3 = (1 / 11 Ω) + (1 / 7 Ω ) + (1 / 20 Ω) 1 / Req = 0.283766 Ω-1 Req = 1 / (0.283766 Ω-1) Req = 3.52 Ω (rounded from 3.524027 Ω) Now that the equivalent resistance is known, the current in the battery can be determined using the Ohm's law equation. In using the Ohm's law equation (ΔV = I • R) to determine the current in the circuit, it is important to use the battery voltage for ΔV and the equivalent resistance for R. The calculation is shown here: Itot = ΔVbattery / Req = (12 V) / (3.524027 Ω) Itot = 3.41 Amp (rounded from 3.4051948 Amp) The 12 V battery voltage represents the gain in electric potential by a charge as it passes through the battery. The charge loses this same amount of electric potential for any given pass through the external circuit. That is, the voltage drop across each one of the three resistors is the same as the voltage gained in the battery: ΔV battery = ΔV 1 = ΔV 2 = ΔV 3 = 12 V There are three values left to be determined - the current in each of the individual resistors. Ohm's law is used once more to determine the current values for each resistor - it is simply the voltage drop across each resistor (12 Volts) divided by the resistance of each resistor (given in the problem statement). The calculations are shown below. I1 = ΔV1 / R1 I1 = (12 V) / (11 Ω) I1 = 1.091 Amp I2 = ΔV 2 / R2 I2 = (12 V) / (7 Ω) I2 = 1.714 Amp I3 = ΔV 3 / R3 I3 = (12 V) / (20 Ω) I3 = 0.600 Amp As a check of the accuracy of the mathematics performed, it is wise to see if the calculated values satisfy the principle that the sum of the current values for each individual resistor is equal to the total current in the circuit (or in the battery). In other words, is Itot = I1 + I2 + I3 ? Is Itot = I1 + I2 + I3 ? Is 3.405 Amp = 1.091 Amp + 1.714 Amp + 0.600 Amp ? Is 3.405 Amp = 3.405 Amp? Yes!!

1. As more and more resistors are added in parallel to a circuit, the equivalent resistance of the circuit ____________ (increases, decreases) and the total current of the circuit ____________ (increases, decreases).

Answers:As more and more resistors are added in parallel to a circuit, the equivalent resistance of the circuit decreases and the total current of the circuit increases. Reasoning=Adding more resistors in parallel is equivalent to providing more branches through which charge can flow. Even though the added branches offer resistance to the flow of charge, the overall resistance decreases due to the fact that there are additional pathways available for charge flow. The fraction of the total charge which encounters a single resistor is now less. The additional branches mean that the circuit can sustain a greater current.

. Which adjustments could be made to the circuit below that would decrease the current in the cell? List all that apply. a. Increase the resistance of bulb X. b. Decrease the resistance of bulb X. c. Increase the resistance of bulb Z. d. Decrease the resistance of bulb Z. e. Increase the voltage of the cell (somehow). f. Decrease the voltage of the cell (somehow). g. Remove bulb Y.

Answers=A,C,F,G The current in the battery is dependent upon the electric potential difference across the battery (V) and the total or equivalent resistance of the circuit (Req). A decrease in V (choice F) and an increase in Req would lead to a decrease in the current at the battery location. The overall resistance can be increased by increasing the resistance of any of the light bulbs (choices A and C) or by reducing the number of branches (choice G)

Electric potential difference AKA Voltage

By definition, the electric potential difference is the difference in electric potential (V) between the final and the initial location when work is done upon a charge to change its potential energy

Current

Current is the rate at which charge flows past a point on a circuit.

Equation for Current

Current=I=Q/t

Electric Current

Electric Current in the external circuit is directed from the positive to the negative terminal.

First Variable Affecting Electrical Resistance

First, the total length of the wires will affect the amount of resistance. The longer the wire, the more resistance that there will be. There is a direct relationship between the amount of resistance encountered by charge and the length of wire it must traverse. After all, if resistance occurs as the result of collisions between charge carriers and the atoms of the wire, then there is likely to be more collisions in a longer wire. More collisions mean more resistance.

Symbol of Current

I Is to represent the quantity current.

EXAMPLE

If three resistors are placed in parallel branches and powered by a 12-volt battery, then the voltage drop across each one of the three resistors is 12 volts. A charge flowing through the circuit would only encounter one of these three resistors and thus encounter a single voltage drop of 12 volts.

Extra Info

In a parallel circuit, charge divides up into separate branches such that there can be more current in one branch than there is in another. Nonetheless, when taken as a whole, the total amount of current in all the branches when added together is the same as the amount of current at locations outside the branches. The rule that current is everywhere the same still works, only with a twist. The current outside the branches is the same as the sum of the current in the individual branches. It is still the same amount of current, only split up into more than one pathway.

Parallel Circuits

In a parallel circuit, each device is placed in its own separate branch. The presence of branch lines means that there are multiple pathways by which charge can traverse the external circuit. Each charge passing through the loop of the external circuit will pass through a single resistor present in a single branch. When arriving at the branching location or node, a charge makes a choice as to which branch to travel through on its journey back to the low potential terminal.

Series Connection

In conducting the lab activity, distinctly different observations are made for the two types of circuits. A series circuit can be constructed by connecting light bulbs in such a manner that there is a single pathway for charge flow; the bulbs are added to the same line with no branching point. As more and more light bulbs are added, the brightness of each bulb gradually decreases. This observation is an indicator that the current within the circuit is decreasing.

Parallel Circuits

It is clear from observing the indicator bulbs in the above diagrams that the addition of more resistors causes the indicator bulb to get brighter. For parallel circuits, as the number of resistors increases, the overall current also increases. This increase in current is consistent with a decrease in overall resistance. Adding more resistors in a separate branch has the unexpected result of decreasing the overall resistance! If an individual bulb in a parallel branch is unscrewed from its socket, then there is still current in the overall circuit and current in the other branches. Removing the third bulb from its socket has the effect of transforming the circuit from a three-bulb parallel circuit to a two-bulb parallel circuit. If the appliances in a household kitchen were connected in parallel, then the refrigerator could function without having to have the dishwasher, toaster, garbage disposal and overhead lights on. One appliance can work without the other appliances having to be on. Since each appliance is in its own separate branch, turning that appliance off merely cuts off the flow of charge to that branch. There will still be charge flowing through the other branches to the other appliances. Quite obviously, the appliances in a home are wired with parallel connections.

Equation for Resistance

R=Pxl/a where L represents the length of the wire (in meters), A represents the cross-sectional area of the wire (in meters2), and represents the resistivity of the material (in ohm•meter). Consistent with the discussion above, this equation shows that the resistance of a wire is directly proportional to the length of the wire and inversely proportional to the cross-sectional area of the wire. As shown by the equation, knowing the length, cross-sectional area and the material that a wire is made of (and thus, its resistivity) allows one to determine the resistance of the wire.

Resistance

Resistance is the hindrance to the flow of charge

Second Variable Affecting Electrical Resistance

Second, the cross-sectional area of the wires will affect the amount of resistance. Wider wires have a greater cross-sectional area. Water will flow through a wider pipe at a higher rate than it will flow through a narrow pipe. This can be attributed to the lower amount of resistance that is present in the wider pipe. In the same manner, the wider the wire, the less resistance that there will be to the flow of electric charge. When all other variables are the same, charge will flow at higher rates through wider wires with greater cross-sectional areas than through thinner wires.

Resistance of material

Silver 1.59 x 10-8 Copper 1.7 x 10-8 Gold 2.2 x 10-8 Aluminum 2.8 x 10-8 Tungsten 5.6 x 10-8 Iron 10 x 10-8 Platinum 11 x 10-8 Lead 22 x 10-8 Nichrome 150 x 10-8 Carbon 3.5 x 10-5 Polystyrene 107 - 1011 Polyethylene 108 - 109 Glass 1010 - 1014 Hard Rubber 1013 As seen in the table, there is a broad range of resistivity values for various materials. Those materials with lower resistivities offer less resistance to the flow of charge; they are better conductors. The materials shown in the last four rows of the above table have such high resistivity that they would not even be considered to be conductors.

Series Connection

So for series circuits, as more resistors are added the overall current within the circuit decreases. This decrease in current is consistent with the conclusion that the overall resistance increases. A final observation that is unique to series circuits is the effect of removing a bulb from a socket. If one of three bulbs in a series circuit is unscrewed from its socket, then it is observed that the other bulbs immediately go out. In order for the devices in a series circuit to work, each device must work. If one goes out, they all go out. Suppose that all the appliances in a household kitchen were all connected in series. In order for the refrigerator to work in that kitchen, the toaster oven, dishwasher, garbage disposal and overhead light would all have to be on. In order for one device in series to work, they all must work. If current is cut from any one of them, it is cut from all of them. Quite obviously, the appliances in the kitchen are not connected in series.

Equivalent Resistance

The actual amount of current always varies inversely with the amount of overall resistance. There is a clear relationship between the resistance of the individual resistors and the overall resistance of the collection of resistors.

Charge Flow

The average drift speed of an electron is very, very slow,

Equivalent Resistance #2

The equivalent resistance of a circuit is the amount of resistance that a single resistor would need in order to equal the overall effect of the collection of resistors that are present in the circuit

Charge Rate

The rate at which charge (current) flows is everywhere the same.

Equivalence

The rate at which charge flows into a node is equal to the sum of the flow rates in the individual branches beyond the node.

Units for Current

The standard metric unit for current is the ampere

Put in equation form, this principle would be expressed as

Vbattery = V1 = V2 = V3 = ...

Two types of connections

When there are two or more electrical devices present in a circuit with an energy source, there are a couple of basic means by which to connect them. They can be connected in series or connected in parallel. Suppose that there are three light bulbs connected together in the same circuit. If connected in series, then they are connected in such a way that an individual charge would pass through each one of the light bulbs in consecutive fashion. When in series, charge passes through every light bulb. If connected in parallel, a single charge passing through the external circuit would only pass through one of the light bulbs. The light bulbs are placed within a separate branch line, and a charge traversing the external circuit will pass through only one of the branches during its path back to the low potential terminal. The means by which the resistors are connected will have a major effect upon the overall resistance of the circuit, the total current in the circuit, and the current in each resistor. In Lesson 4, we will explore the effect of the type of connection upon the overall current and resistance of the circuit.

Current has a direction. By convention, current is in the direction that?

a. + charges move b. - electrons move c. + electrons move Answer=A Reasoning=By convention, the electric current direction is the direction which positive charge would move. In wires, the actual charge carriers are negatively charged electrons. Nonetheless, the convention used for the direction of current is based on the direction which positive charges would move.

The diagram at the right depicts a conducting wire. Two cross-sectional areas are located 50 cm apart. Every 2.0 seconds, 10 C of charge flow through each of these areas. The current in this wire is ____ A.

a. 0.10 b. 0.25 c. 0.50 d. 1.0 e. 5.0 f. 20 g. 10 h. 40 i. none of these Answer=E Reasoning=Current is the ratio of charge to time. The quantity of charge passing through a cross section in 2 seconds is 10 C. The ratio of charge to time is I = Q / t = ( 10 C) / ( 2 s) = 5 C/s = 5 Ampere

Use your understanding of the mathematical relationship between work, potential energy, charge and electric potential difference to complete the following statements:

a. A 9-volt battery will increase the potential energy of 1 coulomb of charge by ____ joules. b. A 9-volt battery will increase the potential energy of 2 coulombs of charge by ____ joules. c. A 9-volt battery will increase the potential energy of 0.5 coulombs of charge by ____ joules. d. A ___-volt battery will increase the potential energy of 3 coulombs of charge by 18 joules. e. A ___-volt battery will increase the potential energy of 2 coulombs of charge by 3 joules. f. A 1.5-volt battery will increase the potential energy of ____ coulombs of charge by 0.75 joules. g. A 12-volt battery will increase the potential energy of ____ coulombs of charge by 6 joules. Answer= a. A 9-Volt battery will increase the potential energy of 1 Coulomb of charge by 9 Joules. b. A 9-Volt battery will increase the potential energy of 2 Coulombs of charge by 18 Joules. c. A 9-Volt battery will increase the potential energy of 0.5 Coulombs of charge by 4.5 Joules. d. A 6 -Volt battery will increase the potential energy of 3 Coulombs of charge by 18 Joules. e. A 1.5 -Volt battery will increase the potential energy of 2 Coulombs of charge by 3 Joules. f. A 1.5 Volt battery will increase the potential energy of 0.5 Coulombs of charge by 0.75 Joules. g. A 12 Volt battery will increase the potential energy of 0.5 Coulombs of charge by 6 Joules.

Complete the following statements:

a. A current of one ampere is a flow of charge at the rate of _______ coulomb per second. b. When a charge of 8 C flows past any point along a circuit in 2 seconds, the current is ________ A. c. If 5 C of charge flow past point A (diagram at right) in 10 seconds, then the current is _________ A. d. If the current at point D is 2.0 A, then _______ C of charge flow past point D in 10 seconds. e. If 12 C of charge flow past point A in 3 seconds, then 8 C of charge will flow past point E in ________ seconds. f. True or False: The current at point E is considerably less than the current at point A since charge is being used up in the light bulbs. Answers= To answer all these questions, use the mathematical equation for current: I = Q / t a. A current of one ampere is a flow of charge at the rate of 1 coulomb per second. b. When a charge of 8 coulombs flows past any point along a circuit in 2 seconds, the current is 4 A. c. If 5 coulombs of charge flow past point A (diagram at right) in 10 seconds, then the current is 0.5 A. d. If the current at point D is 2.0 A, then 20 coulombs of charge flow past point D in 10 seconds. e. If 12 coulombs of charge flow past point A in 3 seconds, then 8 coulombs of charge will flow past point E in 2 seconds. (The current is 12 C / 3 s or 4 Amperes at point A. Since current is everywhere the same, it is also 4 Amperes at point E. So the ratio of Q to t is 4 C / s.) f. False. The current is everywhere the same within an electric circuit.

Which of the following is true about the electrical circuit in your flashlight?

a. Charge moves around the circuit very fast - nearly as fast as the speed of light. b. The battery supplies the charge (electrons) that moves through the wires. c. The battery supplies the charge (protons) that moves through the wires. d. The charge becomes used up as it passes through the light bulb. e. The battery supplies energy that raises charge from low to high voltage. f. ... nonsense! None of these are true. Answer=E Reasoning=As emphasized on this page, the battery supplies the energy to move the charge through the battery, thus establishing and maintaining an electric potential difference. The battery does not supply electrons nor protons to the circuit; those are already present in the atoms of the conducting material. In fact, there would be no need to even supply charge at all since charge does not get used up in an electric circuit; only energy is used up in an electric circuit.

A current is said to exist whenever?

a. a wire is charged b. a battery is present c. electric charges are unbalanced d. electric charges move in a loop Answer=D Reasoning=Current is the rate at which charge flows. Charge will not flow in a circuit unless there is an energy source capable of creating an electric potential difference and unless there is a closed conducting loop through which the charge can move.

If a battery provides a high voltage, it can ____.

a. do a lot of work over the course of its lifetime b. do a lot of work on each charge it encounters c. push a lot of charge through a circuit d. last a long time Answer=B Reasoning=The electric potential difference or voltage of a battery is the potential energy difference across its terminals for every Coulomb of charge. A high voltage battery maximizes this ratio of energy/charge by doing a lot of work on each charge it encounters.

Moving an electron within an electric field would change the ____ the electron

a. mass of b. amount of charge on c. potential energy of Answer=C Reasoning=When a force is required to move an electron in the direction of an electric field, its electrical potential energy increases. On the other hand, an electron moving opposite the direction of the electric field will decrease its electrical potential energy. This is because the electric field direction is in the direction which a positive charge spontaneously moves. An electron is negatively charged.

If an electrical circuit were analogous to a water circuit at a water park, then the battery voltage would be comparable to _____.

a. the rate at which water flows through the circuit b. the speed at which water flows through the circuit c. the distance that water flows through the circuit d. the water pressure between the top and bottom of the circuit e. the hindrance caused by obstacles in the path of the moving water Answer=D Reasoning=The battery establishes an electric potential difference across the two ends of the external circuit and thus causes the charge to flow. The battery voltage is the numerical value of this electric potential difference. In an analogous manner, it is the difference in water pressure between the top of the water slide and the bottom of the water slide that the water pump creates. This difference in water pressure causes water to flow down the slide. Because of the similarity between electric potential difference in an electric circuit and water pressure in a water park, the quantity electric potential difference is sometimes referred to as electric pressure.

The drift velocity of mobile charge carriers in electric circuits is?

a. very fast; less than but very close to the speed of light b. fast; faster than the fastest car but nowhere near the speed of light c. slow; slower than Michael Jackson runs the 220-meters d. very slow; slower than a snail Answer=D Reasoning=The average speed of an electron within a circuit is very, very slow. This is due primarily to the countless collisions with the fixed atoms in the wire. Actual drift speeds depend upon numerous factors. A typical drift speed would be about 1 meter per hour.

Effects

it was emphasized that the act of adding more resistors to a parallel circuit results in the rather unexpected result of having less overall resistance. Since there are multiple pathways by which charge can flow, adding another resistor in a separate branch provides another pathway by which to direct charge through the main area of resistance within the circuit. This decreased resistance resulting from increasing the number of branches will have the effect of increasing the rate at which charge flows (also known as the current.

Voltage Drops for Parallel Branches

whatever voltage boost is acquired by a charge in the battery is lost by the charge as it passes through the resistors of the external circuit. The total voltage drop in the external circuit is equal to the gain in voltage as a charge passes through the internal circuit. In a parallel circuit, a charge does not pass through every resistor; rather, it passes through a single resistor. Thus, the entire voltage drop across that resistor must match the battery voltage. It matters not whether the charge passes through resistor 1, resistor 2, or resistor 3, the voltage drop across the resistor that it chooses to pass through must equal the voltage of the battery