Simple Circuit

Q. A dielectic of dielectric constant $K$ completely fills the gap between the plates of a parallel plate capacitor whose capacitance is equal to $C_0$ , when dielectric is absent. Find the mechanical work that must be done against electric forces for extracting the dielectric out of the capacitor , if voltage $\left(V\right)$ of the capacitor is maintained constant.

1. $\frac{1}{2}(K-1)C_0{V}^2$
2. $\frac{(2K-1)C_0{V}^2}{2}$
3. $\frac{1}{2}(\frac{1}{K}-1)C_0{V}^2$
4. $\frac{K}{2}{C}_0{V}^2$

Q. A uniform wire of resistance $72\Omega$ is bent in the form of a hexagon (regular), then the effective resistance between A & B is

1. $10\Omega$
2. $6\Omega$
3. $8\Omega$
4. $9\Omega$

Q. A real voltmeter of resistance 1000 ohm is used to measure potential difference across a resistance of 20 ohm. The percentage error in potential difference measured by the voltmeter is nearly equal to 1. 1% 2. 2% 3. 5% 4. 10%

Q. Consider the circuit shown in the figure. The current i₃ is equal to

1. 5 amp
2. 3 amp
3. – 3 amp
4. $-\frac{5}{6}$ amp

Q. The equivalent resistance between $\text{A}$ and $\text{B}$ is

1. zero if $V_A>V_B$ and $54\Omega$ if $V_A<V_B$
2. $18\Omega$, if $V_A<V_B$
3. zero if $V_A<V_B$ and $54\Omega$ if $V_A>V_B$
4. $36\Omega$, if $V_A>V_B$

Q. Consider the circuit shown in the figure. The current i₃ is equal to

1. 5 amp
2. 3 amp
3. – 3 amp
4. $-\frac{5}{6}$ amp

Q. Two coaxial coils are very close to each other and their mutual inductance is $3\text{H}.$ If a current $i_1=2\sin 30t\text{A}$ is passing through the first coil, then find the peak value of induced emf in the second coil.

1. $180\text{V}$
2. $0\text{V}$
3. $\frac{180}{\sqrt{2}}\text{V}$
4. $90\text{V}$

Q. The capacitor $C_1$ in the figure initially carries a charge $q_0$. When the switch $S_1$ and $S_2$ are closed, capacitor $C_1$ is connected to a resistor $R$ and a second capacitor $C_2$ which initially does not carry any charge. The current $i$, through resistor $R$ as a function of time $t$ is represented as:

1. $i=\frac{q_0}{C_{1}R}{e}^{[\frac{-t(C_1+C_2)}{C_1{C}_{2}R}]}$
2. $i=\frac{2q_0}{C_{1}R}{e}^{[\frac{-t}{C_{2}R}]}$
3. $i=\frac{q_0}{C_1}{e}^{[\frac{-t(C_1+C_2)}{R}]}$
4. $i=\frac{2q_0}{C_{2}R}{e}^{[\frac{-t}{C_{1}R}]}$

Q. What is the direction of current flow in this circuit?

1. Clockwise
2. Anticlockwise
3. Into the plane of the circuit
4. Out of the plane of the circuit.

Q. Derive the resistance in parallel circuit relation: Delta R/R^2 = delta R1/R1^2 + delta R2/R2^2

Q.
Find current through $2\Omega$ resistance

1. 7.5A
2. 2.5A
3. 5A
4. 10A