Q. No.The charge flowing through a resistance \(R\) varies with time \(t\) as \(Q=at-bt^2,\) where \(a\) and \(b\) are positive constants. The total heat produced in \(R\) is:
1.
\(\dfrac{a^3R}{3b}\)
2.
\(\dfrac{a^3R}{2b}\)
3.
\(\dfrac{a^3R}{b}\)
4.
\(\dfrac{a^3R}{6b}\)
| 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. | \(\frac{\sigma_1 \sigma_2}{\sigma_1+\sigma_2}\) |
\(\mathrm{A, B}~\text{and}~\mathrm{C}\) are voltmeters of resistance \(R\), \(1.5R\) and \(3R\) respectively as shown in the figure above. When some potential difference is applied between \(\mathrm{X}\) and \(\mathrm{Y}\), the voltmeter readings are \({V}_\mathrm{A}\), \({V}_\mathrm{B}\) and \({V}_\mathrm{C}\) respectively. Then:
| 1. | \({V}_\mathrm{A} ={V}_\mathrm{B}={V}_\mathrm{C}\) | 2. | \({V}_\mathrm{A} \neq{V}_\text{B}={V}_\mathrm{C}\) |
| 3. | \({V}_\mathrm{A} ={V}_\mathrm{B}\neq{V}_\mathrm{C}\) | 4. | \({V}_\mathrm{A} \ne{V}_\mathrm{B}\ne{V}_\mathrm{C}\) |
| 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. | \(0.5~\Omega\) |
| 1. | is zero. |
| 2. | depends upon the choice of the two materials of the thermocouple. |
| 3. | is negative. |
| 4. | is positive. |
See the electrical circuit shown in this figure. Which of the following is a correct equation for it?
| 1. | \(\varepsilon_1-(i_1+i_2)R-i_1r_1=0\) |
| 2. | \(\varepsilon_2-i_2r_2-\varepsilon_1-i_1r_1=0\) |
| 3. | \(-\varepsilon_2-(i_1+i_2)R+i_2r_2=0\) |
| 4. | \(\varepsilon_1-(i_1+i_2)R+i_1r_1=0\) |
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