# Worksheet: Impedance and Power of Alternating-Current Circuits

In this worksheet, we will practice calculating the impedance of RLC alternating current circuits and how phase angle depends on impedance and frequency.

Q1:

The figure shows an RLC circuit.

What is the total impedance of the circuit?

What is the phase angle between the current and the emf in the circuit?

Q2:

A 20-Ω resistor, 50-µF capacitor, and 30-mH inductor are connected in series with an ac source of amplitude 10 V and frequency 125 Hz.

What is the impedance of the circuit?

What is the amplitude of the current in the circuit?

What is the phase constant of the current?

How much energy is dissipated by the resistor in 2.5 s?

Q3:

An alternating current generator is connected to a device whose internal circuits are not known. We only know current and voltage outside the device, as shown in the diagram. What is the power dissipated by the circuit?

Q4:

In an series circuit, = 200 Ω, = 1.0 H, = 50 µF, = 120 V, and = 50 Hz. What is the power output of the source?

Q5:

A 7.0-mH inductor is connected across a 60-Hz ac source whose voltage amplitude is 50 V.

What is the maximum current through the inductor?

How much does the phase of the current through the potential difference lead the phase of the current across the inductor?

Q6:

An RLC series circuit consists of a 50- resistor, a 200-F capacitor, and a 120-mH inductor whose coil has a resistance of 20 Ω. The source for the circuit has an rms emf of 240 V at a frequency of 60 Hz.

Calculate the rms voltage across the resistor.

Calculate the rms voltage across the capacitor.

Calculate the rms voltage across the inductor.

Q7:

An ac source is modelled by , where and .

Find the rms current when this source is connected across a 20-µF capacitor.

Find the rms current when this source is connected across a 20-mH inductor.

Find the rms current when this source is connected across a 50-Ω resistor.

Q8:

A resistor and capacitor are connected in series across an ac generator. The emf of the generator is given by , where , , , and .

What is the impedance of the circuit?

What is the amplitude of the current through the resistor?

Q9:

An RLC circuit includes a resistor of resistance 0.50 kΩ and an inductor of inductance 0.20 H. The circuit is connected to a 100 V, 0.50 kHz source.

Find the average power dissipated in the resistor if the capacitance of the circuit is 2.0 µF.

Find the average power dissipated in the resistor if the capacitance of the circuit is 0.20 µF.