Q. No.The equivalent resistance between \(A\) and \(B\) is:
| 1. | \(20~\Omega\) | 2. | \(4.8~\Omega\) |
| 3. | \(10~\Omega\) | 4. | \(5~\Omega\) |
Subtopic: Â Combination of Resistors |
Level 3: 35%-60%
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A thin circular conducting wire is connected at \(A,B\) where the smaller arc \(AB\) represents \(\dfrac14^{\text{th}}\) of the circumference. A current flows from \(A\) to \(B,\) dividing into two branches \(i_1\) and \(i_2\) at \(A.\) The ratio \(i_1:i_2\) equals:
| 1. | \(3\) | 2. | \(4\) |
| 3. | \(\dfrac13\) | 4. | \(1\) |
Subtopic: Â Combination of Resistors |
 57%
Level 3: 35%-60%
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Find the equivalent resistance of the circuit between \(A,B\) shown in the figure when
(a) terminals \(C,D\) are disconnected (switch \(K\) is open)
(b) terminals \(C,D\) are connected (switch \(K\) is closed)
1. \(2.5~\Omega,~2.5~\Omega\)
2. \(2.5~\Omega,~2.4~\Omega\)
3. \(2.4~\Omega,~2.5~\Omega\)
4. \(2.4~\Omega,~2.4~\Omega\)
(a) terminals \(C,D\) are disconnected (switch \(K\) is open)
(b) terminals \(C,D\) are connected (switch \(K\) is closed)
1. \(2.5~\Omega,~2.5~\Omega\)
2. \(2.5~\Omega,~2.4~\Omega\)
3. \(2.4~\Omega,~2.5~\Omega\)
4. \(2.4~\Omega,~2.4~\Omega\)
Subtopic: Â Combination of Resistors |
 57%
Level 3: 35%-60%
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Given below are two statements:
Several resistances \(R_1, R_2, .........R_n\) are connected in parallel. The equivalent resistance of the combination is \(R\).
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. |
Subtopic: Â Combination of Resistors |
 59%
Level 3: 35%-60%
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Two identical rheostats \((A~\&~B)\) are connected in series, and their tapping points (exactly in the middle) are also connected to each other through a resistance \(R,\) which is also equal to the resistance of either rheostat. The resistance of the system, between \(X\) and \(Y,\) is:
| 1. | \(3R\) | 2. | \(\Large\frac{5R}{2}\) |
| 3. | \(\Large\frac{4R}{3}\) | 4. | \(\Large\frac{3R}{2}\) |
Subtopic: Â Combination of Resistors |
 67%
Level 2: 60%+
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All the resistances to the left of the vertical line \(PQ\) are \(1~\Omega\), while those on the right of line \(PQ\) are \(2~\Omega\) as shown in the figure above. The equivalent resistance between \(A\) and \(B\) is:
| 1. | \(18~\Omega\) | 2. | \(9~\Omega\) |
| 3. | \(4.5~\Omega\) | 4. | \(2.25~\Omega\) |
Subtopic: Â Combination of Resistors |
 70%
Level 2: 60%+
Hints
All the resistances in the circuit shown below are \(2~\Omega.\) The equivalent resistance between \(A\) and \(C\) is:
| 1. | \(4~\Omega\) | 2. | \(2~\Omega\) |
| 3. | \(\dfrac43~\Omega\) | 4. | \(\dfrac{10}3~\Omega\) |
Subtopic: Â Combination of Resistors |
 73%
Level 2: 60%+
Hints
Two resistances of \(4~\Omega\) and \(6~\Omega\) are connected in series and potential difference of \(60~\text V\) is applied to the combination.
| Statement I: | The voltage across each resistor is \(60~\text V.\) |
| Statement II: | The current through each resistor is \(6~\text A.\) |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Â Combination of Resistors |
 78%
Level 2: 60%+
Hints
The equivalent resistance between \(A\) and \(B\) is:
| 1. | \(20~\Omega\) | 2. | \(4.8~\Omega\) |
| 3. | \(10~\Omega\) | 4. | \(5~\Omega\) |
Subtopic: Â Combination of Resistors |
 83%
Level 1: 80%+
Hints
Identical resistances, of value \(R\), each, are connected along the edges of a tetrahedron. If the equivalent resistance of this combination is measured between two vertices, it will be:
| 1. | \(\dfrac{R}{2}\) | 2. | \(\dfrac{R}{4}\) |
| 3. | \(\dfrac{R}{6}\) | 4. | \(2R\) |
Subtopic: Â Combination of Resistors |
 56%
Level 3: 35%-60%
Hints
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