After the switch shown in figure $A$ is closed, there is current $i$ through resistance $R$. Figure $B$ indicates current variation curves $a, b, c$ and $d$ for four sets of values of $R$ and capacitance $C$:
$(i)$ $R_0$ and $C_0$, $(ii)$ $2R_0$ and $C_0$,
$(iii)$ $R_0$ and $2C_0$, $(iv)$ $2R_0$ and $2C_0$.
Which set goes with which curve?
$(i)$ $R_0$ and $C_0$, $(ii)$ $2R_0$ and $C_0$,
$(iii)$ $R_0$ and $2C_0$, $(iv)$ $2R_0$ and $2C_0$.
Which set goes with which curve?
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$(i)$ $\mathrm{i}=\mathrm{i}_{0} \mathrm{e}^{-\mathrm{t} / \mathrm{R}_{0} \mathrm{C}_{0}}=\frac{\mathrm{V}_{0}}{\mathrm{R}_{0}} \mathrm{e}^{-\mathrm{t} / \mathrm{R}_{0} \mathrm{C}_{0}}, \tau=\mathrm{R}_{0} \mathrm{C}_{0}$
$(ii)$ $\mathrm{i}=\mathrm{i}_{0} \mathrm{e}^{-\mathrm{t} / 2 \mathrm{R}_{0} \mathrm{C}_{0}}=\frac{\mathrm{V}_{0}}{2 \mathrm{R}_{0}} \mathrm{e}^{-\mathrm{t} / 2 \mathrm{R}_{0} \mathrm{C}_{0}}, \tau=2 \mathrm{R}_{0} \mathrm{C}_{0}$
$(iii)$ $\mathrm{i}=\mathrm{i}_{0} \mathrm{e}^{-\mathrm{t} / 2 \mathrm{R}_{0} \mathrm{C}_{0}}=\frac{\mathrm{V}_{0}}{\mathrm{R}_{0}} \mathrm{e}^{-\mathrm{t} / 2 \mathrm{R}_{0} \mathrm{C}_{0}}, \tau=2 \mathrm{R}_{0} \mathrm{C}_{0}$
$(iv)$ $\mathrm{i}=\mathrm{i}_{0} \mathrm{e}^{-\mathrm{t} / 4 \mathrm{R}_{0} \mathrm{C}_{0}}=\frac{\mathrm{V}_{0}}{2 \mathrm{R}_{0}} \mathrm{e}^{-t / 4 \mathrm{R}_{0} \mathrm{C}_{0}}, \tau=4 \mathrm{R}_{0} \mathrm{C}_{0}$
$(i)$ $-(\mathrm{c})$ $(ii)$ $-(\mathrm{a})$ $(iii)$ $-(\mathrm{d}),$ $(iv)$ $-(\mathrm{b})$
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