Twelve wires of equal resistance \(R\) are connected to form a cube. The effective resistance between two diagonal ends \(A\) and \(E\) will be:
1. \(\frac{5 R}{6}\)
2. \(\frac{6 R}{5}\)
3. \(12 R\)
4. \(3 R\)
A constant voltage is applied between the two ends of a uniform metallic wire. Some heat is developed in it. The heat developed doubles if:
1. | both the length and the radius of the wire are halved. |
2. | both the length and the radius of the wire are doubled. |
3. | the radius of the wire is doubled. |
4. | The length of the wire is doubled. |
a. | Conservation of the current density vector. |
b. | Conservation of charge. |
c. | The fact that the momentum with which a charged particle approaches a junction is unchanged (as a vector) as the charged particle leaves the junction. |
d. | The fact that there is no accumulation of charges at a junction. |
Which of the above statements are correct?
1. (b) and (c)
2. (a) and (c)
3. (b) and (d)
4. (c) and (d)
A charged particle having drift velocity of \(7.5\times10^{-4}~\text{ms}^{-1}\) in an electric field of \(3\times10^{-10}~\text{Vm}^{-1}\), has mobility of:
1. \(2.5\times 10^{6}~\text{m}^2\text{V}^{-1}\text{s}^{-1}\)
2. \(2.5\times 10^{-6}~\text{m}^2\text{V}^{-1}\text{s}^{-1}\)
3. \(2.25\times 10^{-15}~\text{m}^2\text{V}^{-1}\text{s}^{-1}\)
4. \(2.25\times 10^{15}~\text{m}^2\text{V}^{-1}\text{s}^{-1}\)
For the circuit shown in the figure, the current \(I\) will be:
1. \(0.75~\text{A}\)
2. \(1~\text{A}\)
3. \(1.5~\text{A}\)
4. \(0.5~\text{A}\)
Two solid conductors are made up of the same material and have the same length and the same resistance. One of them has a circular cross-section of area and the other one has a square cross-section of area . The ratio is:
1. | \(1.5\) | 2. | \(1\) |
3. | \(0.8\) | 4. | \(2\) |
For the circuit given below, Kirchhoff's loop rule for the loop \(BCDEB\) is given by the equation:
1. | \(-{i}_2 {R}_2+{E}_2-{E}_3+{i}_3{R}_1=0\) |
2. | \({i}_2{R}_2+{E}_2-{E}_3-{i}_3 {R}_1=0\) |
3. | \({i}_2 {R}_2+{E}_2+{E}_3+{i}_3 {R}_1=0\) |
4. | \(-{i}_2 {R}_2+{E}_2+{E}_3+{i}_3{R}_1=0\) |
The equivalent resistance between \(A\) and \(B\) for the mesh shown in the figure is:
1. | \(7.2\) \(\Omega\) | 2. | \(16\) \(\Omega\) |
3. | \(30\) \(\Omega\) | 4. | \(4.8\) \(\Omega\) |
When a \(100\) W, \(240\) V bulb is operated at \(200\) volt, the current in it is:
1. \(0.35~\text{A}\)
2. \(0.42~\text{A}\)
3. \(0.50~\text{A}\)
4. \(0.58~\text{A}\)
For the given circuit, the value of the resistance in which the maximum heat is produced is:
1. \(2~\Omega\)
2. \(6~\Omega\)
3. \(4~\Omega\)
4. \(12~\Omega\)