Answer
We can match up the curves as follows:
(1) (c)
(2) (a)
(3) (d)
(4) (b)
Work Step by Step
We can write an expression for the current after the switch is closed:
$i(t) = \frac{\mathscr{E}}{R}~e^{-\frac{t}{RC}}$
When $t = 0$, then $i = \frac{\mathscr{E}}{R}$
Therefore:
(c) and (d) show the current when $R=R_0$
(a) and (b) show the current when $R=2R_0$
At $t$ increases, if $C$ is smaller, then $i$ decreases more quickly.
Therefore:
(a) and (c) show the current when $C=C_0$
(b) and (d) show the current when $C=2C_0$
We can match up the curves as follows:
(1) (c)
(2) (a)
(3) (d)
(4) (b)
