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Q. No.In an electrical circuit, the voltage is measured as \({V}=(200\pm4)\) volts and the current is measured as \({I}=(20\pm0.2)~\text A.\) The value of the resistance is:
1.
\((10\pm4.2)~\Omega \)
2.
\((10\pm0.3)~\Omega \)
3.
\((10\pm0.1)~\Omega \)
4.
\((10\pm0.8)~\Omega \)
Subtopic: Derivation of Ohm's Law |
51%
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A uniform metal wire of length \(l\) has \(10~\Omega \) resistance. Now this wire is stretched to a length \(2l\) and then bent to form a perfect circle. The equivalent resistance across any arbitrary diameter of that circle is:
| 1. | \(10~\Omega \) | 2. | \(5~\Omega \) |
| 3. | \(40~\Omega \) | 4. | \(20~\Omega \) |
Subtopic: Current & Current Density |
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The given circuit shows a uniform straight wire \(AB\) of \(40 ~\text{cm}\) length fixed at both ends. In order to get zero reading in the galvanometer \(G,\) the free end of \(J\) is to be placed from the end \(B\) at:
| 1. | \(32~\text{cm}\) | 2. | \(8~\text{cm}\) |
| 3. | \(16~\text{cm}\) | 4. | \(24~\text{cm}\) |
Subtopic: Wheatstone Bridge |
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The amplitude of the charge oscillating in a circuit decreases exponentially as \(\mathrm{Q=Q_{0}e}^{-Rt/2L}\) where \({Q}_0\) is the charge at \({t}=0~\text{s}.\)The time at which charge amplitude decreases to \(0.50~{Q}_0\) is nearly:
\((\text{Given that}~ {R=1.5~\Omega,~L=12~\text{mH},~\text{ln}(2)=0.693})\)
1. \(19.01~\text{ms}\)
2. \(11.09~\text{ms}\)
3. \(19.01~\text s\)
4. \(11.09~\text s\)
\((\text{Given that}~ {R=1.5~\Omega,~L=12~\text{mH},~\text{ln}(2)=0.693})\)
1. \(19.01~\text{ms}\)
2. \(11.09~\text{ms}\)
3. \(19.01~\text s\)
4. \(11.09~\text s\)
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The steady-state current in the circuit shown below is:
| 1. | \(0.67~\text A\) | 2. | \(1.5~\text A\) |
| 3. | \(2~\text A\) | 4. | \(1~\text A\) |
Subtopic: Derivation of Ohm's Law |
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A uniform wire of diameter \(d\) carries a current of \(100~\text{mA}\) when the mean drift velocity of electrons in the wire is \(v.\) For a wire of diameter \({\dfrac{d}{2}}\) of the same material to carry a current of \(200~\text{mA},\) the mean drift velocity of electrons in the wire is:
| 1. | \(4v\) | 2. | \(8v\) |
| 3. | \(v\) | 4. | \(2v\) |
Subtopic: Current & Current Density |
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Arrange the following in the order of their resistance.
Choose the correct answer from the options given below:
| A. | (\(0\) to \(1~\text A\)) ranged ammeter. |
| B. | (\(0\) to \(100~\text {mA}\)) ranged milli-ammeter. |
| C. | (\(0\) to \(500~\mu\text A\)) ranged micro-ammeter. |
| D. | (\(0\) to \(100~\text V\)) ranged voltmeter. |
Choose the correct answer from the options given below:
| 1. | \(\mathrm{A > B > C > D}\) | 2. | \(\mathrm{D > C > B > A}\) |
| 3. | \(\mathrm{D > A > B > C}\) | 4. | \(\mathrm{C > B > A > D}\) |
Subtopic: Derivation of Ohm's Law |
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There are two heaters \(A\) and \(B.\) The heater \(A\) takes time \(t_1\) to boil a given quantity of water, while \(B\) takes time \(t_2\) to boil the same quantity of water across the same supply voltage. If the two heaters are connected in series, the time taken by this combination to boil the same quantity of water will be:
| 1. | \(\large\dfrac{t_1t_2}{t_1+t_2}\) | 2. | \(t_1+t_2\) |
| 3. | \({\large\dfrac12}(t_1+t_2)\) | 4. | \(\large\dfrac{t_1t_2}{2(t_1+t_2)}\) |
Subtopic: Heating Effects of Current |
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The value of \(R\) in the given circuit when there is no current in the \(5 ~\Omega\) resistor is:
| 1. | \(12~\Omega\) | 2. | \(9~ \Omega\) |
| 3. | \(3~ \Omega\) | 4. | \(2~ \Omega\) |
Subtopic: Wheatstone Bridge |
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The equivalent resistance \(R_{AB}\) between points \(A\) and \(B\) in the given network is:
| 1. | \(1R\) | 2. | \({\dfrac35}R\) |
| 3. | \({\dfrac78}R\) | 4. | \({\dfrac58}R\) |
Subtopic: Combination of Resistors |
72%
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