Question

An emf of 100 V is applied to a series RC circuit in which the resistance is 200 ohms & the capacitance is 10/10000 farad. Determine the charges q(t)=0. Also determine the current i(t).

Answer 1

Answer on Question #66378-Physics-Mechanics-Relativity

An emf of $100\mathrm{V}$ is applied to a series RC circuit in which the resistance is 200 ohms and the capacitance is 10-4 farads. Determine the charge $q(t)$ on the capacitor if $q(0) = 0$. Also determine the current $i(t)$.

Solution

The charge on capacitor is

$$q(t) = Q \left(1 - e^{-\frac{t}{\tau}}\right).$$ $$\tau = RC = (200)(10^{-4}) = 0.02\,s.$$ $$Q = CE = (10^{-4})(100) = 0.01\,C.$$

Thus,

$$q(t) = 0.01(1 - e^{-50t})\,C.$$

The current is

$$i(t) = I e^{-\frac{t}{\tau}}.$$ $$I = \frac{Q}{\tau} = \frac{0.01}{0.02} = 0.5\,A.$$

Thus,

$$i(t) = 0.5 e^{-50t}\,A.$$

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