Q. No.A wire is connected to form an equilateral triangle \(ABC\), each side having a resistance of \(4~\Omega\). The vertex \(C\) is maintained at zero volts (\(V_C=0\)), and currents flowing in at \(A\) and \(B\) are as shown in the figure. The ratio of the potentials at \(D\) and \(E\) \(\Big(i.e.~\frac{V_D}{V_E}\Big)\) equals:
1.
\(\dfrac31\)
2.
\(\dfrac21\)
3.
\(\dfrac11\)
4.
\(\dfrac53\)
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If the tapping point \(C\) is moved so that the length \(BC\) is reduced to half its initial value, then the voltage across the \(15~\Omega\) resistor,
| 1. | increases by \(1\) V |
| 2. | decreases by \(1\) V |
| 3. | increases by \(3\) V |
| 4. | decreases by \(3\) V |
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1. \(1~\text{A}\)
2. \(2~\text{A}\)
3. \(0.5 ~\text{A}\)
4. \(0.25~\text{A}\)
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| 1. | \(2~\text{A}\) | 2. | \(1~\text{A}\) |
| 3. | \(1.8~\text{A}\) | 4. | \(2.2~\text{A}\) |
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| 1. | \(100~\Omega\) | 2. | \(50~\Omega\) |
| 3. | \(200~\Omega\) | 4. | \(400~\Omega\) |
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Several resistances \(R_1, R_2, .........R_n\) are connected in parallel. The equivalent resistance of the combination is \(R\).
| Assertion (A): | The fractional error in \(R\) is most affected by that of the smallest resistance in the combination, other things being equal. |
| Reason (R): | In parallel, the conductances add. The contribution to the overall error in the conductance is largest for the largest conductance or the smallest resistance. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
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1. \(|E-E_1|<|E-E_2|\)
2. \(|E+E_1|<|E+E_2|\)
3. \(|E-E_1|>|E-E_2|\)
4. \(|E+E_1|>|E+E_2|\)
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The thermal energy generated in the resistance due to Joule heating is:
1. \(240\) J
2. \(480\) J
3. \(160\) J
4. \(320\) J
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| 1. | \(18~\Omega\) | 2. | \(9~\Omega\) |
| 3. | \(4.5~\Omega\) | 4. | \(2.25~\Omega\) |
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| Assertion (A): | In the Wheatstone Bridge shown in the figure, if the resistances in opposite arms are switched (i.e. \(Q, R\) are exchanged) then the bridge remains balanced if it was initially balanced. |
| Reason (R): | The balance condition \(\dfrac P Q\) = \(\dfrac R S\) is not affected if resistances in opposite arms are switched. |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is a correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not a correct explanation of (A). |
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