Question

i would like to know how to solve this step by step

Answer 1

When the capacitor voltage is 75v the switch position is moved to (2) v_c(0) = 75v (the initial capacitor voltage) applying KVL V_c(t) + 1 2(t) + 1 times i(t) = 0 rightarrow v_c(t) + 2i(t) = 0 rightarrow v_c(t) + 2c dv/dt v_c(t) = 0 rightarrow v_c(t) = -2c dv_c(t)/dt rightarrow 2c integral^t_0 dv_c(t)/dv_c(t)(= -integral^t_0 dt rightarrow ln v_c(t) = -t/2c + k when t = 0 v_c(0) = 75 ln(75) = k rightarrow v_c(t) = 75 e^- t/2c t = 0.7 times RC = 0.7 times 1 times 10^6 times 1 times 10^- 6 = 0.7 v_c(t) = 75 e^- 0.7 = 37.34v