First slide

KVL

Question

A capacitor is charged using an external battery with a resistance x in series. The dashed line shows the variation of ln I with respect to time t. lf the resistance is changed to 2x, the new graph will be

Moderate

A

P
B

Q
C

R
D

S

Solution

$I = \frac{ε}{R} e^{- t / RC}$
$\log_{e} I = \log_{e} \frac{ε}{R} - \frac{t}{RC} \log_{e} e \Rightarrow \ln I = \ln (\frac{ε}{R}) - \frac{t}{RC}$
$Slope = - \frac{t}{RC}; y intercept = \ln (\frac{ε}{r})$
If resistance is made doubled, both slope and y intercept decrease in magnitude.

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