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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:  Heating Effects of Current |
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Two cells having emfs \(3\) V and \(2\) V are connected in parallel and they give an emf of \(0.5\) V in the same sense as \(3\)\(-\) cell. The internal resistances of the cells are \(r_1\) and \(r_2\) respectively. If one cell is reversed, their combined emf becomes \(2.5\) V. The ratio of their internal resistances \(\Big(\dfrac{r_1}{r_2}\Big) \) is:
1. \(1\)
2. \(\dfrac12\)
3. \(\dfrac21\)
4. \(\sqrt2\)
Subtopic:  Grouping of Cells |
 67%
From NCERT
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The resistance of each arm of the Wheatstone’s bridge is \(10~\Omega.\) If a resistance of \(10~\Omega\) is connected in series with a galvanometer, then the equivalent resistance across the battery will be:
1. \(10~\Omega\) 2. \(15~\Omega\)
3. \(20~\Omega\) 4. \(40~\Omega\)
Subtopic:  Wheatstone Bridge |
 74%
From NCERT
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The current in a simple series circuit is \(5.0\) A. When an additional resistance of \(2.0\) \(\Omega\)  is inserted, the current decreases to \(4.0\) A. The original resistance of the circuit  was:
1. \(1.25\) \(\Omega\)
2. \(8\) \(\Omega\)
3. \(10\) \(\Omega\)
4. \(20\) \(\Omega\)

Subtopic:  Combination of Resistors |
 82%
From NCERT
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Given below are two statements: 
Statement I: Kirchhoff’s current law is a consequence of the conservation of energy as applied to electric circuits.
Statement II: Kirchhoff’s voltage law is a consequence of the conservation of charge.
 
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:  Kirchoff's Voltage Law |
 70%
From NCERT
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A wire made of a metal of uniform resistivity \(1.0\times 10^{-6}~\Omega{\text{-m}}\)  is \(2.0~\text{m}\) long and has a diameter of \(2.0\times 10^{-3}~\text{m}.\). What is the electrical resistance of this length of the wire?
1. \(\dfrac {2.0 ~\times~10^{-3}}{\pi} ~\Omega\) 2. \(5.0 ~\times~10^{-13}\pi~\Omega\)
3. \(\dfrac {1.0}{2\pi}~\Omega\) 4. \(\dfrac{2.0}{\pi}~\Omega\)
Subtopic:  Derivation of Ohm's Law |
 82%
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A resistor has a resistance of \(5.0 ~\Omega.\) There is a direct current of \(10~\text{A}\) in the resistor. What is the power dissipated by the resistor?
1. \(50~\text{W}\)
2. \(2500~\text{W}\)
3. \(20~\text{W}\)
4. \(500~\text{W}\)
Subtopic:  Heating Effects of Current |
 90%
From NCERT
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Two copper wires of length \(l\) and \(2l\) have radii \(r\) and \(2r\) respectively. What is the ratio of their specific resistances?
1. \(1:2\)
2. \(2:1\)
3. \(1:1\)
4. \(1:3\)
Subtopic:  Derivation of Ohm's Law |
 66%
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Two metallic wires of identical dimensions are connected in series. If \(\sigma _1\) and \(\sigma_2\) are the conductivities of these wires respectively, the effective conductivity of the combination is: 
 
1. \(\dfrac{\sigma_1 \sigma_2}{\sigma_1+\sigma_2} \) 2. \(\dfrac{2 \sigma_1 \sigma_2}{\sigma_1+\sigma_2} \)
3. \(\dfrac{\sigma_1+\sigma_2}{2 \sigma_1 \sigma_2} \) 4. \(\dfrac{\sigma_1+\sigma_2}{\sigma_1 \sigma_2}\)
Subtopic:  Combination of Resistors |
 69%
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In the circuit shown in the figure, applying Kirchhoff's loop rule to the loop \(abca\) gives:
          
1. \(-12+7I_1-4I_3=0\)
2. \(12+7I_1-4I_3=0\)
3. \(-12-7I_1+4I_3=0\)
4. \(-12+7I_1+4I_3=0\)
Subtopic:  Kirchoff's Voltage Law |
 64%
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