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, $P_1$

$(B)$ 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, $Q_2$

IIT 2022, Advanced
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Case $(i)$

When both switches are open equivalent resistance in circuit $1$

$R _{ c _1}=\frac{16}{11} \Omega$

Equivalent resistance in circuit $2$

$R_{c=}=\frac{6}{11} \Omega$

For voltage source

$P=\frac{V^2}{R}$

$P \propto \frac{1}{R}$

$R_{c_e}>R_{c_e}$

$\Rightarrow P_2>P_1 \text { (Option (A) correct) }$

For congtant curent source

$P =i^2 R$

$P \propto R$

$\Rightarrow P _1> P _2 \text { (Option (B) coerect) }$

Cros-$II$

When swirch is cloced

$R _{c_1}^{\prime}=\frac{5}{11} \Omega$

$R _{c_1}^{\prime}=\frac{1}{2} \Omega$

$R _{c_0}^{\prime}< R _{c_0}$

For voltage source

$P \times \frac{1}{ R } \Rightarrow Q_2> P _2 \text { (Oprion (C) correct) }$

$ R_{c_0}^{\prime}>R_{c_1}^{\prime}$

For current source $P \propto R$.

$Q_1>Q_2 \text { (Option (D) also comrect) }$

art

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