Physics - Current Electricity Question with Solution | TestHub

Resistance of arm $PQ$ and $ST$ becomes ineffective as $P\&Q$ and $S\&T$ are at the same potential. The equivalent circuit is as shown in the figure.
The resistance of the upper arm $R_1=2\Omega +2\Omega +2\Omega =6\Omega$
The resistance of the lower arm $R_2=4\Omega +4\Omega +4\Omega =12\Omega$ Equivalent resistance of the circuit, $\begin{array}{l}{R}_{\mathrm{eq}}=\frac{R_1{R}_2}{R_1+R_2}=\frac{(6\Omega )(12\Omega )}{6\Omega +12\Omega }=4\Omega \\ \therefore I_1=\frac{12\mathrm{V}}{4\Omega }=3\mathrm{A}\\ I_2=\left(\frac{12}{6+12}\right)\times 3=2\mathrm{A}\\ I_3=I_1-I_2=1\mathrm{A}\end{array}$ Potential difference across $A$ and $P$, $\begin{array}{l}{V}_A-V_P=I_2\times 2\Omega =(2A)(2\Omega )\\ 12V-V_P=4V\text{ or }{V}_P=8V\end{array}$ Potential difference across $A$ and $Q$, $\begin{array}{l}{V}_A-V_Q=I_3\times 2\Omega =(1A)(4\Omega )\\ 12V-V_Q=4V\\ V_Q=12\mathrm{V}-4\mathrm{V}=8\mathrm{V}\end{array}$ Potential difference across $P$ and $S$, $\begin{array}{l}{V}_P-V_S=(2A)(2W)=4V\\ 8V-V_S=4V\Rightarrow V_S=4V\\ \therefore V_S<V_Q\end{array}$