Question

The charge across the capacitor in two different $RC$ circuits $1$ and $2$ are plotted as shown in the figure. Choose the correct statement(s) related to the two circuits.

• A. Both the capacitors are charged to the same charge
• B. The emf's of cells in both the circuit are equal
• C. The emf's of the cells may be different
• D. The emf $E_1$ is more than $E_2$

Answer 1

Answer: (A), (C)

The correct options are
A Both the capacitors are charged to the same charge
C The emf's of the cells may be different

The charge on capacitor at any time t is $q=q_{max}(1-e^{-t/CR})$

As the $q_{max}$ of the both curve is same so both capacitor will be charged to same charge.

As (2) curve take more time for maximum charging so time constant of curve (2) is greater than (1). i.e, ${\tau }_2>{\tau }_1\Rightarrow C_2{R}_2>C_1{R}_1$

As $q_{max}$ is same for both curve so $C_1{E}_1=C_2{E}_2$

Since $C_1$ and $C_2$ are different so emf of both cell may be different.

now $E_1=\left(C_2/C_1\right)E_2>\left(R_1/R_2\right)E_2$

If $R_1>R_2$ , then $E_1>E_2$.