The figure above shows a circuit containing an electromotive force (a battery),

Question

The figure above shows a circuit containing an electromotive force (a battery), a capacitor with a capacitance of C farads (F), and a resistor with a resistance of R ohms (Ohm). The voltage drop across the capacitor is Q/C, where Q is the charge (in coulombs), so in this case Kirchhoff's Law gives RI + Q/C = E(t). Since the current is I = dQ/dt, we have RdQ/dt + 1/C Q = E(t). Suppose the resistance is 10 Ohm, the capacitance is 0.2F, a battery gives a constant voltage of E(t) = 50V, and the initial charge is Q(0) = 0C. Find the charge and the current at time t. O(t) =, I(t) = .

Explanation / Answer

Q = Qoe-t/RC
where Q is charge at any time t , Qo is the maximum charge , t is the time , R is resistance and C is the capacitance.
Similarly
I = Ioe-t/RC
where I is the current at any time t , Io is the maximum current
Now we can put the value of above variables and find the value at any time t

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