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 $6 V$ is connected across A and B in both circuits, $P_1 < P_2$.
• B. When a constant current source of $2 Amp$ is connected across A and B in both circuits, $P_1>P_2$.
• C. When a voltage source of $6 V$ is connected across A and B in Circuit-1, $Q_1>P_1$.
• D. When a constant current source of $2 Amp$ 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 $P \propto R$
$Q _1> Q _2$