For the circuit shown, 30 Ω 0.5 F 0.25 H el + v 60u(1) V (+ 20 Ω +) 30u(t) V the generalized solution of the step response of the capacitor voltage is -0.167t v(t) = V; + A1e 47.83t + A2e volts

4.) For the circuit below, the input Vi is a 10V pulse that lasts for 1 second. R = 1060, C = 44.4nF, L = 1mH. Assume all initial conditions are zero. a.) Find the equation for Vi(t) b.) Find Vi(s) c.) Find the s-domain equation for voltage across the capacitor, Vo(s). Find the voltage across the capacitor, v.(t) V(+ |1₁ C HH so

My teacher said that the equation v(t) for Vcap (in image) will be V = -1/C integral of i(t) + v(initial). My question is, my teacher has said that the '-' infront of the 1/C is because the current flows into the negative terminal of the capacitor. But in the answer my teacher has put v(initial) as +20 and not -20, even though the 20V across the capacitor is also negative to positive as shown in the image. So why is the v(initial) put as +20 and not -20? Thank you.

Please answer in typing format

The problem asks us to evaluate the integral, I attempted to solve it but it was not correct. Could I please get an explanation as to how to fix my approach, and how to solve this problem step by step?

After being closed for a long time the switch in the RC circuit shown below opens at time t=18 ms. Find io (t) for t > 0 ms. For full credit include the equations and a plot describing io (t). Hint: use superposition to find the contributions of each source. 1 k. t=18 ms 1 kΩ + 10 μ VC 1 k2 6 V 10 cos(200t) V io