Question

An electrical circuit is shown in figure-$3.371$. The resistance of each voltmeter is infinite and each ammeter is $100\, \Omega$. The charge on the capacitor of $100 \,\mu F$ in steady sate is $4\, mC$. Choose which of the following statements is/are correct regarding the given circuit :

• A. Reading of voltmeter $V_{2}$ is $16 \,V$
• B. Reading of ammeter $A_{1}$ is zero and $A_{2}$ is $1 / 25\, A$
• C. Reading of voltmeter $V_{1}$ is $40 \,V$
• D. EMF of the ideal cell is $48\, V$

Answer 1

Answer: (A), (C), (D)

In steady state current through branch of capacitor is zero.
Thus current flows through $200\, \Omega$ and $900 \,\Omega$ and ammeter $A_{2}$ in series combination.
Potential difference across the capacitor is given as
$V_{C}=\frac{q}{C}=\frac{4 \times 10^{-3}}{100 \times 10^{-6}}=40 \,V$
This is also potential drop across $900\, \Omega$ resistance and $100\, \Omega$ ammeter $A_{2}$ in series of which the total resistance is $1000\, \Omega$.
This $1000\, \Omega$ and $200 \,\Omega$ resistances are in series so we use
$V_{2}=V_{200 \Omega}=\frac{V_{1000 \Omega}}{5}=\frac{40}{5}=8\,V$
Thus battery EMF is given as
$E=V_{1000 \Omega}+V_{200 \Omega}=48 \,V$
Current through the battery is given as
$i =\frac{E}{R}$
$\Rightarrow i =\frac{48}{1200}=\frac{1}{25}\, A$