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 = 1.0 ext ms .

Step-by-step solution

The discharging of a capacitor is given by the equation: q(t) = q₀ e^ -t / where = RC is the time constant of the circuit. Given values are C = 10 F , R = 10 , q₀ = 60 C , and t = 1.0 ms = 10⁻³ s . Calculating the time constant : = RC = 10 10 10⁻⁶ = 10⁻⁴ s Substituting the values into the discharging equation: q(t) = 60 e^ -10⁻³ / 10⁻⁴ C q(t) = 60 e⁻¹⁰ C Using the approximate value e¹⁰ 22026 : q(t) = 60 22026 C 0.00272 C Rounding to the nearest given option, the charge is approximately 0.003 C .