A filament bulb \((500~\text{W},100~\text{V})\) is to be used in a \(230~\text{V}\) main supply. When a resistance\(R\) is connected in series, the bulb works perfectly and consumes \(500~\text{W}.\) The value of \(R\) is:
1.
\(230~\Omega\)
2.
\(46~\Omega\)
3.
\(26~\Omega\)
4.
\(13~\Omega\)
| 1. | \(\dfrac{a^3R}{3b}\) | 2. | \(\dfrac{a^3R}{2b}\) |
| 3. | \(\dfrac{a^3R}{b}\) | 4. | \(\dfrac{a^3R}{6b}\) |
Two metal wires of identical dimensions are connected in series. If \(\sigma_1~\text{and}~\sigma_2\)
| 1. | \(\frac{2\sigma_1 \sigma_2}{\sigma_1+\sigma_2}\) | 2. | \(\frac{\sigma_1 +\sigma_2}{2\sigma_1\sigma_2}\) |
| 3. | \(\frac{\sigma_1 +\sigma_2}{\sigma_1\sigma_2}\) | 4. | \(\frac{\sigma_1 \sigma_2}{\sigma_1+\sigma_2}\) |
A circuit contains an ammeter, a battery of \(30~\text{V},\) and a resistance \(40.8~\Omega\) all connected in series. If the ammeter has a coil of resistance \(480~\Omega\) and a shunt of \(20~\Omega,\) then the reading in the ammeter will be:
1. \(0.5~\text{A}\)
2. \(0.02~\text{A}\)
3. \(2~\text{A}\)
4. \(1~\text{A}\)
\({A, B}~\text{and}~{C}\) are voltmeters of resistance \(R,\) \(1.5R\) and \(3R\) respectively as shown in the figure above. When some potential difference is applied between \({X}\) and \({Y},\) the voltmeter readings are \({V}_{A},\) \({V}_{B}\) and \({V}_{C}\) respectively. Then:
| 1. | \({V}_{A} ={V}_{B}={V}_{C}\) | 2. | \({V}_{A} \neq{V}_{B}={V}_{C}\) |
| 3. | \({V}_{A} ={V}_{B}\neq{V}_{C}\) | 4. | \({V}_{A} \ne{V}_{B}\ne{V}_{C}\) |
| 1. | current density | 2. | current |
| 3. | drift velocity | 4. | electric field |
The figure given below shows a circuit when resistances in the two arms of the meter bridge are \(5~\Omega\) and \(R\), respectively. When the resistance \(R\) is shunted with equal resistance, the new balance point is at \(1.6l_1\). The resistance \(R\) is:
| 1. | \(10~\Omega\) | 2. | \(15~\Omega\) |
| 3. | \(20~\Omega\) | 4. | \(25~\Omega\) |
2. \(0.1~\text{A}\)
3. \(2.0~\text{A}\)
4. \(1.0~\text{A}\)
If power dissipated in the \(9~\Omega\) resistor in the circuit shown is \(36\) W, the potential difference across the \(2~\Omega\) resistor will be:
1. \(8\) V
2. \(10\) V
3. \(2\) V
4. \(4\) V
A current of \(2~\text{A}\) flows through a \(2~\Omega\) resistor when connected across a battery. The same battery supplies a current of \(0.5~\text{A}\) when connected across a \(9~\Omega\) resistor. The internal resistance of the battery is:
| 1. | \(\dfrac{1}{3}~\Omega\) | 2. | \(\dfrac{1}{4}~\Omega\) |
| 3. | \(1~\Omega\) | 4. | \(0.5~\Omega\) |
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