Wire's Resistance

The discharge characteristic of a capacitor as formulated below has been produced by considering a series $RC$ circuit in which a capacitor at full charge is made to discharge at time, $t = 0$ when the plates are connected through a resistor $R$ . We need to find this $R$ .

$E = E_{0} e^{-t/RC}$ ... (i)

$E = \frac{1}{3E_{0}}$ , $C = 2.0 \mu F$ and $t = 4.4 \mu s$ are given. Using these in (i), we get:

$\frac{1}{3E_{0}} = E_{0} e^{-4.4/2R}$

$\implies$ $ln(\frac{1}{3}) = e^{-4.4/2R}$

$\implies$ $-1.1 = -\frac{4.4}{2R}$

$\implies$ $R = 2 \Omega$ (rounded off)