Question

In Circuit-1 and Circuit-2 shown in the figures, $R_1=1\Omega ,R_2=2\Omega$ and $R_3=3\Omega .P_1$ and $P_2$ are the power dissipations in Circuit-1 and Circuit-2 when the switches $S_1$ and $S_2$ are in open conditions, respectively.
$Q_1$ and $Q_2$ are the power dissipations in Circuit-1 and Circuit-2 when the switches $S_1$ and $S_2$ are in closed conditions, respectively.

Which of the following statement(s) is(are) correct?

• A. When a voltage source of $6V$ is connected across A and B in both circuits, $P_1<P_2$.
• B. When a constant current source of $2Amp$ is connected across A and B in both circuits, $P_1>P_2$.
• C. When a voltage source of $6V$ is connected across A and B in Circuit-1, $Q_1>P_1$.
• D. When a constant current source of $2Amp$ is connected across A and B in both circuits, $Q_2<Q_1$

Answer 1

Answer: (A), (B), (C)

Case (i)
When both switches are open equivalent resistance in circuit 1
$R_{C_1}=\frac{16}{11}\Omega$
Equivalent resistance in circuit 2
$R_{C_2}=\frac{6}{11}\Omega$
For voltage source
$P=\frac{V^2}{R}$
$P\propto \frac{1}{R}$
$R_{C_1}>R_{C_2}$
$\Rightarrow P_2>P_1\text{ (Option (A) correct) }$
For constant current source
$P=i^{2}R$
$P\propto R$
$\Rightarrow P_1>P_2\text{ (Option (B) correct) }$
Case-II
When switch is closed
$R_{C_1}^{\prime }=\frac{5}{11}\Omega$
$R_{C_2}^{\prime }=\frac{1}{2}\Omega$
$R_{C_1}^{\prime }<R_{C_1}$
For voltage source
$P\propto \frac{1}{R}\Rightarrow Q_1>P_1(\text{ Option }(C)\text{ correct) }$
$\&R_{C_1}^{\prime }>R_{C_2}^{\prime }$
For current source $P\propto R$
$Q_1>Q_2$