Question

The figure shows a part of the circuit at $t=0$. Charge on the capacitor as a function of time is given by $q=3(1-e^{-t})$ $C$. At $t=0$, mark the correct statement(s).

• A. Current through branch containing capacitor is $3A$.
• B. Current through R is $\frac{17}{4}A$
• C. The potential of P is $17V$
• D. The value of R is $2\Omega$

Answer 1

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

The correct options are
A Current through branch containing capacitor is $3A$.
B Current through R is $\frac{17}{4}A$
C The potential of P is $17V$


Let $q=0C(\text{at}t=0)i=\frac{dq}{dt}=3e^{-t}=3A(\text{at}t=0)\text{Applying KVL along APC at t=0,}\Rightarrow 20-\frac{q}{C}-(1\times i)-i_{2}R=0\Rightarrow 20-3=R{i}_2\Rightarrow R{i}_2=17....\left(i\right)$

$\text{Applying KVL along BPC}20-2+(i-i_2)1-R{i}_2=0\Rightarrow 20-2+3-i_2-R{i}_2=0\Rightarrow i_2=20-2+3-17\Rightarrow i_2=4A$

So from ($i$) and ($ii$)
$\Rightarrow R=\frac{17}{4}\Omega$

Potential at P,
$\Rightarrow V_p=V_A-i\times 1=20-1\times 3=17V$