AC Theory, Level 2, Lesson 2

Given the circuit and parameters shown, solve for the following: (Round the FINAL answers to at least two decimal places in the specified unit.)

Iₜ = E / R Iₜ = 25 / 1,000 Iₜ = 0.025 A = 25 mA * Eₜ = √Eᵣ² + E꜀² Eₜ = √25² + 40² Eₜ = 47.17 V * X꜀ = E꜀ / Iₜ X꜀ = 40 / 0.025 X꜀ = 1,600 Ω * C = 1 / 2πƒX꜀ C = 2π × 200 × 1,600 C = 0.000 000 497 F = 497 nF * PF = Eᵣ / Eₜ x 100 PF = 25 / 47.17 x 100 PF = 52.99 %

What is the total resistance of the circuit shown?

11 Ω

What is the total capacitance of the circuit shown? Calculate to the nearest whole number of the unit specified.

55 nF

For a series RC circuit, the ? must be the same through all parts of the circuit.

Current

Consider the series circuit shown below. Drag the labels to the appropriate vectors on the correct vector diagram below.

Er is adjacent, Ec is opposite, Et is hypotenuse.

A series circuit has a large Xc and small R. The power factor is close to 100%.

False

When solving a series RC circuit, the voltage is the reference.

False

Using the circuit shown below, label the sides of the power triangle with the correct label and value.

Side A is 490 W, Side B is 735 VAR, Side C is 883.4 VA

1.) A circuit that contains resistance and capacitance is called an RC circuit.

True

A series circuit has a large R and small Xc. The phase angle is close to 0°.

True

Given the circuit and parameters shown, solve for the following: (Round the FINAL answers to at least two decimal places in the specified unit.)

X꜀ = 1 / 2πƒC X꜀ = 2π × 60 × 0.000 000 47 X꜀ = 5,643.79 Ω * Z = √R² + X꜀² Z = √4,700² + 5.643.79² Z = 7,344.55 Ω * Iₜ = Eₜ / Z Iₜ = 30 / 7,344.55 Iₜ = 0.00409 A = 4.09 mA * Eᵣ = Iₜ x R Eᵣ = 0.00409 x 4,700 Eᵣ = 19.22 V * E꜀ = Iₜ x X꜀ E꜀ = 0.00409 x 5,642.79 E꜀ = 23.08 V * PF = R / Z x 100 PF = 4,700 / 7,344.55 x 100 PF = 63.99 %

Given the circuit and parameters shown, solve for the following: (Round the FINAL answers to at least two decimal places in the specified unit.)

X꜀ = 1 / 2πƒC X꜀ = 2π × 60 × 0.000 015 X꜀ = 176.84 Ω * Z = √R² + X꜀² Z = √140² + 176.84² Z = 225.55 Ω * Iₜ = E / Z Iₜ = 120 / 225.55 Iₜ = 0.53204 A = 532.04 mA * E꜀ = Iₜ x X꜀ E꜀ = 0.53204 x 176.84 E꜀ = 94.08 V * Eᵣ = Iₜ x R Eᵣ = 0.53204 x 140 Eᵣ = 74.48 V * PF = R / Z x 100 PF = 140 / 225.55 x 100 PF = 62.07 % * θ = cos⁻¹(R/Z) θ = cos⁻¹(140 / 225.55) θ = 51.63°

Given the circuit and parameters shown, solve for the following: (Round the FINAL answers to at least two decimal places in the specified unit.)

Z = √R² + X꜀² Z = √40² + 60² Z = 72.11 Ω * Eᵣ = Iₜ x R Eᵣ = 3.5 x 40 Eᵣ = 140 V * E꜀ = Iₜ x X꜀ E꜀ = 3.5 x 60 E꜀ = 210 V * Eₜ = Iₜ x Z Eₜ = 3.5 x 72.11 Eₜ = 252.39 V * Pᵣₑₐ꜀ₜ = Iₜ x E꜀ Pᵣₑₐ꜀ₜ = 3.5 x 210 Pᵣₑₐ꜀ₜ = 735 VAR * Pₐₚₚ = Iₜ x Eₜ Pₐₚₚ = 3.5 x 252.39 Pₐₚₚ = 883.36 VA * Pₜᵣᵤₑ = Iₜ x Eᵣ Pₜᵣᵤₑ = 3.5 x 140 Pₜᵣᵤₑ = 490 W * PF = R / Z x 100 PF = 40 / 72.11 x 100 PF = 55.47 % * θ = cos⁻¹(R/Z) θ = cos⁻¹(40 / 72.11) θ = 56.31°

A series circuit contains 40 ohms of resistance (R) and 70 ohms of capacitive reactance (Xc). When 100 volts AC are applied, how much current flows? (Round the FINAL answer to two decimal places.)

Z = √R² + X꜀² Z = √40² + 70² Z = 80.62 Ω * I = E / Z I = 100 / 88.62 I = 1.24 A

Label the correct impedance triangle to show the vector relationships for an RC series circuit.

Z is hypotenuse, R is adjacent, Xc is opposite.

A circuit has a resistor and a capacitor connected in series and operating at a certain frequency. If the frequency is increased, the capacitive reactance ? .

decreases

A circuit has a resistor and a capacitor connected in series and operating at a certain frequency. If the frequency is increased, the impedance ? .

decreases

A circuit has a resistor and a capacitor connected in series and operating at a certain frequency. If the frequency is increased, the phase angle ? .

decreases

A circuit has a resistor and a capacitor connected in series and operating at a certain frequency. If the frequency is increased, the current ? .

increases

A circuit has a resistor and a capacitor connected in series and operating at a certain frequency. If the frequency is increased, the power factor ? .

increases