Chapter (4) : Resistors

Grouping of resistors: Equivalent resistors

(Req): It is the resistance of the equivalent resistor for the grouping of the individual resistors connected in series, parallel or in a complex circuit.

Ohm's law, graph

- If we intend to find the resistance of a resistor we conduct an experiment to study the variation of voltage as a function of current. The graph in the adjacent figure is obtained. - The graph, giving the variation of the voltage U across the terminals of a resistor as function of the current I traversing it is called: " Voltage - current characteristic of a resistor" The voltage-current of a resistor is a straight line passing through the origin whose slope is the resistance R. This verifies ohm's law that I and U are directly proportional such that the proportionality constant is R. slope = R

In a graph, you should always put:

- Scale - Title - Graph Itself - plotting the 2 points on the graph in order to calculate the slope (resistance graphically)

According to ohm's law

- When R is constant, U and I are directly proportional. - When U is constant, R and I are inversely proportional. - When I is constant, U and R are directly proportional.

Finding the resistance graphically

--> It is a st. line passing through the origin (0,0) choosing 2 points e.g A(1,2), and B(2,4) slope = (Yb - Ya) / (Xb - Xa) = (Ub - Ua) / Ib - Ia) = (4-2) / (2-1) = 2/1 = 2 ohm = Resistance of the resistor (R) } Graphically

Characteristics of a resistor

1) Any resistor is characterized by a physical quantity called "resistance" whose symbol is "R". In S.I units, resistance "R" is measured in Ohm. (Omega) which we denote by the symbol: (picture) 1K(ohm) = 1,000 ohm 2) The two terminals of a resistor are identical.

Fun Fact

Amount of energy on earth is always constant, since energy cannot be created or destroyed just converted from one form to another - Isaac Newton

Benefit of a resistor

Heat and protects the appliances as the fuse

Remark

In a closed circuit, composed of certain number of resistors (regardless of their grouping) whose equivalent resistance is Req, and a generator that delivers a current Imain in the main branch of the circuit, and whose voltage is Ug: Ug = Imain x Req

Rheostate

It is a resistor that we can vary it's resistance Symbol: (put Rh in the box)

Definition of a resistor

It is an electric component used to liberate (release) heat in a circuit or a load that acts as a voltage divider.

Function

It resists the flow of electrons in a closed circuit, thus resulting in the decrease of the values of both current and voltage, and for that it is used to protect appliances (installations).

Conversion of Ohm

K(ohm) --> Ohm --> m(ohm) --> x 10^3 / 10^3 <---

Measuring resistance of a resistor

Measuring instrument: Resistance is measured using a multimeter functioning as an Ohmmeter. Connections: It is connected in parallel across the terminals of a resistor. Scale: Select the resistance range then choose the scale to be slightly greater than the value to be measured. - In an electric circuit, we may represent a resistor by either one of the following: (put R in the box)

Another way to represent a resistor

Put "R" above it

Parallel connection

R1 and R2 are connected in parallel. We can replace them by one resistor whose resistance is Req, which is equal to the reciprocal of the sum of reciprocals of resistances of both resistors. The new resistor will produce the same effect. Not special case, for all parallel connections: 1/Req = 1/R1 + 1/R2 Special case (only 2 parallel) 1/Req = R1 + R2 / R1 x R2 So, Req = R1 x R2 / R1 + R2 (refer to the worksheet) on the calculater: 1/answer = Req

Series connection

R1 and R2 are connected in series. We can replace them by one resistor whose resistance is Req, which is equal to the sum of resistances of both resistors. The new resistor will produce the same effect. Req = R1 + R2 (Refer to the worksheet to see figure)

Variable DC generator

Symbol:

How to find the highest resistor based on the graph

The line steeper; nearer to the y-axis is the larger resistance --> larger slope

Ohm's law of a resistor

The voltage across a resistor is the product of its resistance by the current it carries. U = R x I Where: U is the voltage in Volts (V) I is the current in Ampere (A) R is the resistance in ohms (ohm symbol, the horse shoe)

Ohm's law formulas

U = R x I R = U/I I = U/R where: I: it is the current traversing the resistor (A) U: Voltage across the resistor (V) R: Resistance of the resistor (ohm)

When Resistance changes

Voltage and Current changes and varies

Important Note

When drawing a graph from a table, don't convert, draw based on table info

Equation of a st.line passing through the origin

y= ax U = aI U = RxI a --> slope verrifying ohm's law