Q. No.A wire of resistance \(12~ \Omega \text{m}^{-1}\) is bent to form a complete circle of radius \(10~\text{cm}\). The resistance between its two diametrically opposite points, \(A\) and \(B\) as shown in the figure, is:
1. \(0.6\pi~\Omega\)
2. \(3\pi ~\Omega\)
3. \(61 \pi~ \Omega\)
4. \(6\pi~\Omega\)
1. \(0.6\pi~\Omega\)
2. \(3\pi ~\Omega\)
3. \(61 \pi~ \Omega\)
4. \(6\pi~\Omega\)
2. \(-r\) and \(E\)
See the electrical circuit shown in this figure. Which of the following is a correct equation for it?
| 1. | \(\varepsilon_1-(i_1+i_2)R-i_1r_1=0\) |
| 2. | \(\varepsilon_2-i_2r_2-\varepsilon_1-i_1r_1=0\) |
| 3. | \(-\varepsilon_2-(i_1+i_2)R+i_2r_2=0\) |
| 4. | \(\varepsilon_1-(i_1+i_2)R+i_1r_1=0\) |
A current of \(3~\text{A}\) flows through the \(2~\Omega\) resistor shown in the circuit. The power dissipated in the \(5~\Omega\) resistor is:
| 1. | \(4~\text{W}\) | 2. | \(2~\text{W}\) |
| 3. | \(1~\text{W}\) | 4. | \(5~\text{W}\) |
1. 1.2 times, 1.1 times
2. 1.21 times, same
3. both remain the same
4. 1.1 times, 1.1 times
1. 6.3 min
2. 8.4 min
3. 12.6 min
4. 4.2 min
A cell can be balanced against 100 cm and 110 cm of potentiometer wire, respectively with and without being short-circuited through a resistance of 10 Ω. Its internal resistance is:
1. 1.0 Ω
2. 0.5 Ω
3. 2.0 Ω
4. zero
1. 1.5 V
2. 1.0 V
3. 0.5 V
4. 3.2 V
The total power dissipated in watts in the circuit shown below is:
| 1. | 16 W | 2. | 40 W |
| 3. | 54 W | 4. | 4 W |
Three resistances \(\mathrm P\), \(\mathrm Q\), and \(\mathrm R\), each of \(2~\Omega\) and an unknown resistance \(\mathrm{S}\) form the four arms of a Wheatstone bridge circuit. When the resistance of \(6~\Omega\) is connected in parallel to \(\mathrm{S}\), the bridge gets balanced. What is the value of \(\mathrm{S}\)?
1. \(2~\Omega\)
2. \(3~\Omega\)
3. \(6~\Omega\)
4. \(1~\Omega\)
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