GATE EC 2019 Set 1 Q41 — Electronic Devices

The $\text{RC}$ circuit shown below has a variable resistance $R(t)$ given by the following expression:

$$R(t)=R_{0}\left(1-\frac{t}{T}\right) \text{for} \:\: 0 \leq t < T$$

where $R_{0}=1\: \Omega,$ and $C=1\:F.$ We are also given that $T=3\: R_{0}C$ and the source voltage is $V_{s}=1\: V.$ If the current at time $t=0$ is $1\: A,$ then the current $I(t)$, in amperes, at time $t=T/2$  is __________ (rounded off to $2$ decimal places).