At t = 0 , the plates of a capacitor of capacitance 10 ext F , charged to 60 ext C , are connected together by a wire having a resistance of 10 ext . Determine the charge on the capacitor in the circuit at t = 120 ext s .

Step-by-step solution

The charge on a discharging capacitor at time t is given by the equation: q(t) = q₀ e^ -t/ where the time constant is = RC . Given values are: Initial charge, q₀ = 60 C Resistance, R = 10 Capacitance, C = 10 F Time, t = 120 s Calculating the time constant : = 10 10 F = 100 s Substituting the values into the discharging equation: q(120 s ) = 60 e^ -120/100 q = 60 e^ -1.2 Using the approximate value e^ -1.2 0.301 : q 60 0.301 18.06 C Rounding to the nearest integer, the charge on the capacitor is 18 C .