A ring is made of a wire having a resistance of \(R_0=12~\Omega.\). Find points \(\mathrm{A}\) and \(\mathrm{B}\), as shown in the figure, at which a current-carrying conductor should be connected so that the resistance \(R\) of the subcircuit between these points equals \(\frac{8}{3}~\Omega\)
1. | \(\dfrac{l_1}{l_2} = \dfrac{5}{8}\) | 2. | \(\dfrac{l_1}{l_2} = \dfrac{1}{3}\) |
3. | \(\dfrac{l_1}{l_2} = \dfrac{3}{8}\) | 4. | \(\dfrac{l_1}{l_2} = \dfrac{1}{2}\) |
If power dissipated in the \(9~\Omega\) resistor in the circuit shown is \(36\) W, the potential difference across the \(2~\Omega\) resistor will be:
1. \(8\) V
2. \(10\) V
3. \(2\) V
4. \(4\) V
A current of \(2~\text{A}\) flows through a \(2~\Omega\) resistor when connected across a battery. The same battery supplies a current of \(0.5~\text{A}\) when connected across a \(9~\Omega\) resistor. The internal resistance of the battery is:
1. | \(\dfrac{1}{3}~\Omega\) | 2. | \(\dfrac{1}{4}~\Omega\) |
3. | \(1~\Omega\) | 4. | \(0.5~\Omega\) |
Statement I: | Kirchhoff’s junction law follows the conservation of charge. |
Statement II: | Kirchhoff’s loop law follows the conservation of energy. |
1. | Both Statement I and Statement II are incorrect. |
2. | Statement I is correct but Statement II is incorrect. |
3. | Statement I is incorrect and Statement II is correct. |
4. | Both Statement I and Statement II are correct. |
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. | \(6\pi~\Omega\) |
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. | \(6.3\) min | 2. | \(8.4\) min |
3. | \(12.6\) min | 4. | \(4.2\) min |
The total power dissipated in watts in the circuit shown below is:
1. | \(16\) W | 2. | \(40\) W |
3. | \(54\) W | 4. | \(4\) W |