In the circuit depicted in the figure, the capacitors are initially uncharged. If the switch is closed at t = 0 , determine the charge on the capacitor C₁ as a function of time t .

Step-by-step solution

The given circuit is an RC circuit with two capacitors C₁ and C₂ connected in series with a resistor r . The equivalent capacitance of the series combination is: C_ eq = C₁ C₂ C₁ + C₂ The time constant of the circuit is: = r C_ eq = r C₁ C₂ C₁ + C₂ The maximum steady-state charge on the equivalent capacitor is: q₀ = E C_ eq = E C₁ C₂ C₁ + C₂ The charge on the equivalent capacitor as a function of time is given by the standard charging equation: q(t) = q₀ ( 1 - e^ - t ) Since the capacitors are in series, the charge