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Q. No.Nine similar resistors of resistance \(R\) are connected as shown in the figure. Equivalent resistance between points A and B is:
1. \(\frac{3}{5} R\)
2. \(\frac{4}{3} R\)
3. \(\frac{9}{5} R\)
4. \(R\)
Subtopic: Â Combination of Resistors |
 50%
Level 3: 35%-60%
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The resistance between \(A,B\) is found to be \(500~\Omega\) while that between \(A,C\) is \(400~\Omega.\) The minimum possible value of \(R_2\) is:
1. \(100~\Omega\)
2. \(200~\Omega\)
3. \(400~\Omega\)
4. \(900~\Omega\)
1. \(100~\Omega\)
2. \(200~\Omega\)
3. \(400~\Omega\)
4. \(900~\Omega\)
Subtopic: Â Kirchoff's Voltage Law |
 54%
Level 3: 35%-60%
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The current flowing through the resistance \(R_1\), when \(R_1=R_2\) and \(R_3=R_4\) is:
| 1. | \(\frac{V}{4\left(R_1+R_3\right)}\) | 2. | \(\frac{2 V}{\left(R_1+R_3\right)}\) |
| 3. | \(\frac{V}{\left(R_1+R_3\right)}\) | 4. | \(\frac{V}{2\left(R_1+R_3\right)}\) |
Subtopic: Â Current & Current Density |
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Level 3: 35%-60%
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\(n\) identical cells, each with an EMF \(E\) and internal resistance \(r,\) are connected in series to form a closed circuit. One of the cells, \(A,\) is connected with its polarity reversed. What is the potential difference across each cell (excluding cell \(A\))?
| 1. | \(\dfrac{2E}{n}\) | 2. | \(\dfrac{E}{n}\) |
| 3. | \(\left(\dfrac{n-2}{n}\right)E\) | 4. | \(\left(\dfrac{2n}{n-2}\right)E\) |
Subtopic: Â Grouping of Cells |
Level 4: Below 35%
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Two wires \(A\) and \(B\) are made of the same metal and have equal lengths. The diameter of wire \(A\) is half the diameter of wire \(B.\) If the resistance of wire \(A\) is \(48~\Omega,\) the resistance of wire \(B\) will be:
| 1. | \(96~\Omega\) | 2. | \(192~\Omega\) |
| 3. | \(24~\Omega\) | 4. | \(12~\Omega\) |
Subtopic: Â Derivation of Ohm's Law |
 66%
Level 2: 60%+
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In the circuit shown, current in 5 \(\Omega\) resistor is:
| 1. | 1.5 A from Q to P |
| 2. | 1.5 A from P to Q |
| 3. | 3 A from P to Q |
| 4. | No current flows from Q to P |
Subtopic: Â Kirchoff's Voltage Law |
 70%
Level 2: 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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Current density is the current crossing per unit area. Consider a cylindrical wire of uniform cross-section \(A,\) carrying a current \(I.\) Imagine a cross-section formed by a "\(30^\circ\)-cut" as shown (the wire is not really cut). The current density perpendicular to this cross-section is:
| 1. | \(\dfrac{I}{A}\) | 2. | \(\dfrac{I}{A}~\cos30^\circ\) |
| 3. | \(\dfrac{2I}{A}\) | 4. | \(\dfrac{I}{A}~\sin30^\circ\) |
Subtopic: Â Current & Current Density |
Level 3: 35%-60%
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The potential difference \(V_{AB}\) (in volts) is plotted as a function of the resistance \(R.\) The graph is given by:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Â Derivation of Ohm's Law |
 53%
Level 3: 35%-60%
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\(150\) cc of water taken in an electric kettle boils in \(20\) minutes. If the same amount of water is to be boiled in \(10\) minutes, the length of the heating element will have to be:
| 1. | one fourth | 2. | one third |
| 3. | two times | 4. | one half |
Subtopic: Â Heating Effects of Current |
Level 3: 35%-60%
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