Q. No.A 4 μF capacitor and a resistance of 2.5 MΩ are in series with a 12 V battery. The time after which the potential difference across the capacitor is 3 times the potential difference across the resistor is: [Given ln(2)= 0.693]
1. 13.86 s
2. 6.93 s
3. 7 s
4. 14 s
In the given figure each plate of capacitance C has partial value of charge equal to:
1. CE
2.
3.
4.
The resistance of a wire is \(R\) ohm. If it is melted and stretched to \(n\) times its original length, its new resistance will be:
| 1. | \(nR\) | 2. | \(\frac{R}{n}\) |
| 3. | \(n^2R\) | 4. | \(\frac{R}{n^2}\) |
A light bulb, a capacitor and a battery are connected together as shown below with the switch S initially open. When the switch S is closed, which one of the following is true?
1. The bulb will light up for an instant when
the capacitor starts charging.
2. The bulb will light up when
the capacitor is fully charged.
3. The bulb will not light up at all.
4. The bulb will light up and go off at regular intervals.
A battery consists of a variable number \('n'\) of identical cells having internal resistances connected in series. The terminals of battery are short circuited and the current \(i\) is measured. The graph below that shows the relationship between \(i\) and \(n\) is:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
For a cell, the graph between the potential difference \((V)\) across the terminals of the cell and the current \((I)\) drawn from the cell is shown in the figure below. The emf and the internal resistance of the cell are, respectively:
| 1. | \(2~\text{V}, 0.5 ~\Omega\) | 2. | \(2~\text{V}, 0.4 ~\Omega\) |
| 3. | \(>2~\text{V}, 0.5 ~\Omega\) | 4. | \(>2~\text{V}, 0.4 ~\Omega\) |
Variation of current passing through a conductor with the voltage applied across its ends varies is shown in the diagram below. If the resistance \((R)\) is determined at points \(A\), \(B\), \(C\) and \(D\), we will find that:
| 1. | \(R_C = R_D\) | 2. | \(R_B>R_A\) |
| 3. | \(R_C>R_B\) | 4. | None of these |
\(12\) cells each having the same emf are connected in series with some cells wrongly connected. The arrangement is connected in series with an ammeter and two similar cells which are in series. Current is \(3~\text{A}\) when cells and battery aid each other and is \(2~\text{A}\) when cells and battery oppose each other. The number of cells wrongly connected is/are:
1. \(4\)
2. \(1\)
3. \(3\)
4. \(2\)
The effective resistance between points \(P\) and \(Q\) of the electrical circuit shown in the figure is:
| 1. | \(\frac{2 R r}{\left(R + r \right)}\) | 2. | \(\frac{8R\left(R + r\right)}{\left( 3 R + r\right)}\) |
| 3. | \(2r+4R\) | 4. | \(\frac{5R}{2}+2r\) |
What is the equivalent resistance between terminals \(A\) and \(B\) of the network?
| 1. | \(\dfrac{57}{7}~\Omega\) | 2. | \(8~\Omega\) |
| 3. | \(6~\Omega\) | 4. | \(\dfrac{57}{5}~\Omega\) |
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