Alternating Current Module 25: AC Circuits Dynamic Study Module

A resistor is connected in series with an AC source that provides a sinusoidal voltage of v of t is equal to V times cosine of begin quantity omega times t end quantity, where V is the maximum voltage, omega is the angular frequency, and t is the time. The current that flows through this resistor is described with the function i of t is equal to I times cosine of begin quantity omega times t end quantity, where I is the maximum current in the resistor. What is the rms current in the resistor?

1/ root 2

An alternating-current (AC) source supplies a sinusoidally varying voltage that can be described with the function v of t is equal to V times cosine of begin quantity omega times t end quantity, where V is the maximum voltage, omega is the angular frequency, and t is the time. If the oscillation frequency of this source is 60 Hz, what is the oscillation period?

1/60 s

An alternating-current (AC) source supplies a sinusoidally varying voltage that can be described with the function v of t is equal to V times cosine of begin quantity omega times t end quantity, where V is the maximum voltage, omega is the angular frequency, and t is the time. If the frequency of this source is 60 Hz, what is omega equal to?

2 times pi times 60 Hertz

A fully charged capacitor is connected in series with an inductor, as shown in the figure. When the switch is closed to complete the circuit, the capacitor can discharge through the circuit. What is true about the current in the inductor at the instant the capacitor is fully discharged (when Q = 0 on the capacitor)?

The current in the inductor is at maximum at the instant the capacitor is fully discharged.

The figure shows a transformer that has its primary coil connected to a source of AC current and its secondary coil connected to a device with resistance R. How does the rms current in the device's resistor (I2) compare to the rms current provided by the AC source (I1) if the primary coil has 3 times as many turns of wire as the secondary coil?

I sub 2 = 3I sub 1

The figure shows a transformer that has its primary coil connected to a source of AC current and its secondary coil connected to a device with resistance R. How does the rms current in the device's resistor (I2) compare to the rms current provided by the AC source (I1) if the secondary coil has 4 times as many turns of wire as the primary coil?

I sub 2 = I sub 1/4

A resistor is connected in series with an AC source that provides a sinusoidal voltage of v of t is equal to V times cosine of begin quantity omega times t end quantity, where V is the maximum voltage, omega is the angular frequency, and t is the time. The current supplied by this source that flows through this resistor is described with the function i of t is equal to I times cosine of begin quantity omega times t end quantity, where I is the maximum current. What is the average power supplied by this AC source?

IV/2

A fully charged capacitor is connected in series with an inductor, as shown in the figure. When the switch is closed to complete the circuit, the capacitor can discharge through the circuit. If T is the oscillation period of the LC circuit, how long after closing the switch will the capacitor be fully charged again?

T/2

A resistor with resistance R, a capacitor with capacitance C, and an inductor with inductance L are all connected in series with an AC source that provides a sinusoidal voltage of v of t is equal to V times cosine of begin quantity omega times t end quantity, where V is the maximum voltage, omega is the angular frequency, and t is the time. What is true about the average power loss in the resistor when this R-L-C series circuit is in resonance?

The average power loss in the resistor is a maximum value.

A fully charged capacitor is connected in series with an inductor, as shown in the figure. What happens in the brief amount of time (maybe a few microseconds) just after the switch is closed to complete the circuit?

The capacitor begins to discharge and the current through the inductor increases at the same rate as the charge on the capacitor decreases.

A capacitor is connected in series with an AC source that provides a sinusoidal voltage of v of t is equal to V times cosine of begin quantity omega times t end quantity, where V is the maximum voltage, omega is the angular frequency, and t is the time. What is true about the current that flows in the circuit?

The current in the circuit is out of phase with the voltage and can be described with the function i of t is equal to negative I times sine of begin quantity omega times t end quantity, where I is the maximum current.

A resistor is connected in series with an AC source that provides a sinusoidal voltage of v of t is equal to V times cosine of begin quantity omega times t end quantity, where V is the maximum voltage, omega is the angular frequency, and t is the time. What is true about the current in the resistor?

The current in the resistor is in phase with the voltage and can be described with the function i of t is equal to I times cosine of begin quantity omega times t end quantity, where I is the maximum current.

A resistor with resistance R, a capacitor with capacitance C, and an inductor with inductance L are all connected in series with an AC source that provides a sinusoidal voltage of v of t is equal to V times cosine of begin quantity omega times t end quantity, where V is the maximum voltage, omega is the angular frequency, and t is the time. If the capacitive reactance, XC, is equal to the inductive reactance, XL, what is true about the impedance of this R-L-C series circuit?

The impedance is equal to R.

A fully charged capacitor is connected in series with an inductor, as shown in the figure. When the switch is closed to complete the circuit, the capacitor can discharge through the circuit. This LC oscillator has an oscillation frequency f. If you replaced this inductor with one having twice the inductance, what would happen to the oscillation frequency of the LC oscillator?

The oscillation frequency would decrease by a factor of square root of 2.

A fully charged capacitor is connected in series with an inductor, as shown in the figure. When the switch is closed to complete the circuit, the capacitor can discharge through the circuit. This LC oscillator has an oscillation frequency f. If you replaced this capacitor with one having half the capacitance, what would happen to the oscillation frequency of the LC oscillator?

The oscillation frequency would increase by a factor of square root of 2.

A resistor with resistance R and an inductor with inductance L are connected in series with an AC source that provides a sinusoidal voltage of v of t is equal to V times cosine of begin quantity omega times t end quantity, where V is the maximum voltage, omega is the angular frequency, and t is the time. What happens to the rms current through the resistor as the angular frequency of the AC is increased?

The rms current in the resistor decreases.

A resistor with resistance R and a capacitor with capacitance C are connected in series with an AC source that provides a sinusoidal voltage of v of t is equal to V times cosine of begin quantity omega times t end quantity, where V is the maximum voltage, omega is the angular frequency, and t is the time. What happens to the rms current through the resistor as the angular frequency of the AC is increased?

The rms current in the resistor increases.

A resistor is connected in series with an AC source that provides a sinusoidal voltage of v of t is equal to V times cosine of begin quantity omega times t end quantity, where V is the maximum voltage, omega is the angular frequency, and t is the time. The current that flows through this resistor is described with the function i of t is equal to I times cosine of begin quantity omega times t end quantity, where I is the maximum current in the resistor. What is the rms voltage across the resistor?

V/ root 2

The figure shows a transformer that has its primary coil connected to a source of AC current and its secondary coil connected to a device with resistance R. How does the rms voltage across the device's resistor (V2) compare to the rms voltage of the AC source (V1) if the secondary coil has 4 times as many turns of wire as the primary coil?

V2 = 4V1

The figure shows a transformer that has its primary coil connected to a source of AC current and its secondary coil connected to a device with resistance R. Imagine that we increase the number of turns in the primary coil so that the primary coil has three times as many turns as the secondary coil. How does the rms voltage across the device's resistor (V2) compare to the rms voltage of the AC source (V1) if the primary coil has 3 times as many turns of wire as the secondary coil?

V2 = V1/3

A capacitor with capacitance C is connected in series with an AC source that provides a sinusoidal voltage of v of t is equal to V times cosine of begin quantity omega times t end quantity, where V is the maximum voltage, omega is the angular frequency, and t is the time. If the angular frequency of the AC source is increased from omega to 3 times omega, what happens to the capacitive reactance, XC?

XC decreases by a factor of 3.

A capacitor with capacitance C is connected in series with an AC source that provides a sinusoidal voltage of v of t is equal to V times cosine of begin quantity omega times t end quantity, where V is the maximum voltage, omega is the angular frequency, and t is the time. If a second identical capacitor is wired in series with the first capacitor, what happens to the total capacitive reactance, XC, of the circuit?

XC increases by a factor of 2.

An inductor with inductance L is connected in series with an AC source that provides a sinusoidal voltage of v of t is equal to V times cosine of begin quantity omega times t end quantity, where V is the maximum voltage, omega is the angular frequency, and t is the time. If a second identical inductor is wired in series with the first inductor, what happens to the total inductive reactance, XL, of the circuit?

XL increases by a factor of 2.

An inductor with inductance L is connected in series with an AC source that provides a sinusoidal voltage of v of t is equal to V times cosine of begin quantity omega times t end quantity, where V is the maximum voltage, omega is the angular frequency, and t is the time. If the angular frequency of the AC source is increased from omega to 3 times omega, what happens to the inductive reactance, XL?

XL increases by a factor of 3.

A resistor with resistance R, a capacitor with capacitance C, and an inductor with inductance L are all connected in series with an AC source that provides a sinusoidal voltage of v of t is equal to V times cosine of begin quantity omega times t end quantity, where V is the maximum voltage, omega is the angular frequency, and t is the time. For what angular frequency will this R-L-C series circuit be in resonance?

w = 1/ root LC