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 = 30 ext s .

Step-by-step solution

The time constant of the discharging RC circuit is given by = RC . Substituting the given values: = 10 10 10⁻⁶ s = 100 s The charge on the capacitor during discharging is given by: q = q₀ e^ -t/ Substituting q₀ = 60 C and t = 30 s : q = 60 e^ -30/100 = 60 e^ -0.3 C Using the approximation e^ -0.3 0.74 : q 60 0.74 C = 44.4 C The closest value among the given options is 44 C .