For a series \(\mathrm{LCR}\) circuit, the power loss at resonance is:
1. \(\frac{V^2}{\left[\omega L-\frac{1}{\omega C}\right]}\)
2. \( \mathrm{I}^2 \mathrm{~L} \omega \)
3. \(I^2 R\)
4. \( \frac{\mathrm{V}^2}{\mathrm{C} \omega} \)
A light bulb is rated at \(100~\text{W}\) for a \(220~\text{V}\) AC supply. The RMS current through the bulb is:
1. \(0.243\) A
2. \(0.454\) A
3. \(0.222\) A
4. \(0.312\) A
A \(15.0~\mathrm{\mu F}\) capacitor is connected to a \(220~\mathrm{V}\), \(50~\mathrm{Hz}\) source. If the frequency is doubled, what happens to the capacitive reactance and the current?
1. | the capacitive reactance is halved and the current is doubled. |
2. | the capacitive reactance is doubled and the current is halved. |
3. | the capacitive reactance remains the same and the current is doubled. |
4. | the current remains the same and the capacitive reactance is halved. |
A resistor of \(200~\mathrm{\Omega}\) and a capacitor of \(15.0~\mu\text{F}\) are connected in series to a \(220~\text{V}\), \(50\) Hz AC source. The voltage (RMS) across the resistor and the capacitor are respectively:
1. \( 160.3 ~\text{V}, 160.3 ~\text{V} \)
2. \( 151 ~\text{V}, 151 ~\text{V} \)
3. \( 160.3 ~\text{V}, 151 ~\text{V} \)
4. \( 151 ~\text{V}, 160.3 ~\text{V}\)
1. | \( \frac{\sqrt{3}}{4} \) | 2. | \( \frac{1}{2} \) |
3. | \( \frac{1}{8} \) | 4. | \( \frac{1}{4}\) |
An AC source is rated \(220~\mathrm{V}\), \(50~\mathrm{Hz}\). The average voltage is calculated in a time interval of \(0.01~\mathrm{s}\). It,
1. | must be zero |
2. | may be zero |
3. | is never zero |
4. | \(220\sqrt{2}\) V | is
An AC source rated \(100~\text{V}\) (rms) supplies a current of \(10~\text{A}\) (rms) to a circuit. The average power delivered by the source:
(a) | must be \(1000~\text{W}\). |
(b) | may be \(1000~\text{W}\). |
(c) | may be greater than \(1000~\text{W}\). |
(d) | may be less than \(1000~\text{W}\). |
1. | (a) only |
2. | (b), (c) |
3. | (b), (d) |
4. | (a), (d) |
1. | \(1 / \sqrt{2}\) times the rms value of the AC source. |
2. | the value of voltage supplied to the circuit. |
3. | the rms value of the AC source. |
4. | \(\sqrt{2}\) times the rms value of the AC source. |