Correct answer Carries: 4.
Wrong Answer Carries: -1.
In an AC circuit with only an inductor, what is the phase relationship between the current and the voltage?
In a purely inductive AC circuit, the current lags the voltage by 90°. This is because the inductor opposes changes in current, causing the current to reach its peak after the voltage.
A transformer has \( N_p = 500 \), \( N_s = 250 \). If \( V_s = 120 \, \text{V} \) (rms), what is the primary voltage?
\( \frac{V_s}{V_p} = \frac{N_s}{N_p} \).
\( V_p = V_s \times \frac{N_p}{N_s} = 120 \times \frac{500}{250} = 240 \, \text{V} \).
A series LCR circuit with \( R = 60 \, \Omega \) is at resonance with a \( 240 \, \text{V} \) (rms) source. What is the rms current?
At resonance, \( Z = R = 60 \, \Omega \).
RMS current: \( I = \frac{V}{R} = \frac{240}{60} = 4 \, \text{A} \).
A transformer has \( N_p = 800 \), \( N_s = 400 \). If \( V_s = 110 \, \text{V} \) (rms), what is the primary voltage?
\( V_p = V_s \times \frac{N_p}{N_s} = 110 \times \frac{800}{400} = 220 \, \text{V} \).
A \( 70 \, \Omega \) resistor and \( 30 \, \mu\text{F} \) capacitor are in series with a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the impedance?
\( X_C = \frac{1}{\omega C} = \frac{1}{314 \times 30 \times 10^{-6}} \approx 106.1 \, \Omega \).
\( Z = \sqrt{R^2 + X_C^2} = \sqrt{70^2 + 106.1^2} = \sqrt{4900 + 11257.21} \approx 127.3 \, \Omega \).
A \( 230 \, \text{V} \) (rms) source supplies a \( 115 \, \Omega \) resistor. What is the peak current?
RMS current: \( I = \frac{V}{R} = \frac{230}{115} = 2 \, \text{A} \).
Peak current: \( i_m = \sqrt{2} I = 1.414 \times 2 \approx 2.828 \, \text{A} \).
A \( 22 \, \mu\text{F} \) capacitor is connected to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the rms current?
\( X_C = \frac{1}{\omega C} \), \( \omega = 2\pi \times 50 = 314 \, \text{rad/s} \).
\( C = 22 \times 10^{-6} \, \text{F} \).
\( X_C = \frac{1}{314 \times 22 \times 10^{-6}} \approx 144.7 \, \Omega \).
RMS current: \( I = \frac{V}{X_C} = \frac{220}{144.7} \approx 1.52 \, \text{A} \).
A series LCR circuit has \( R = 35 \, \Omega \), \( X_L = 60 \, \Omega \), \( X_C = 25 \, \Omega \). What is the power factor?
\( Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{35^2 + (60 - 25)^2} = \sqrt{1225 + 1225} = \sqrt{2450} \approx 49.5 \, \Omega \).
Power factor: \( \cos \phi = \frac{R}{Z} = \frac{35}{49.5} \approx 0.707 \).
In an LCR series circuit, what happens to the circuit’s behavior when the frequency is significantly above the resonant frequency?
Above resonance, \( X_L = \omega L \) becomes much larger than \( X_C = \frac{1}{\omega C} \), making the net reactance positive. The circuit behaves as predominantly inductive, with the current lagging the voltage.
In an AC circuit with only a capacitor, what happens to the impedance if the capacitance is decreased?
In a purely capacitive circuit, impedance is \( X_C = \frac{1}{\omega C} \). Decreasing capacitance (\( C \)) increases \( X_C \) because they are inversely proportional, thus increasing the impedance.
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