# Finding the voltage and current at t = 0 using Step Response

The question that I'm trying to solve is as follows:

In the circuit shown below, the switch has been closed for a long time. a) What is v(0) or the voltage across the capacitor immediately after the switch is opened? b) What is i(0) and i1(0)? First, I calculated for the voltage before t = 0 using voltage division. I arrived at v(0-) = 4V. Since the capacitor voltage cannot change instantaneously, I assumed that 4V is the voltage at t=0.

Here's the tricky part. I'm asked to find the current at t = 0. By looking at the diagram, I am certain that the 1-ohm resistor is short-circuited, so I simply dismissed that and used Ohm's Law to find i1(0-) using v = 20 V and R = 4 ohms. In the property of short circuit, the i is equal to 0.

Are my solutions for i1 and i legal to begin with? I'm only confident with 4V as the voltage at t = 0.

• Is the question asking for currents at $0^-$ or $0^+$ (i.e. before or after switch opening) ? Also, what do you mean by 1 ohm resistor is short circuited ? after $t=0$, it is effectively removed from the circuit by the open switch. – AJN Jun 18 at 16:50
• You need to take into account the voltage across the capacitor at t=0+ (you already found this) when calculating the instantaneous current flow in the 4 ohm resistor. – Phil Freedenberg Jun 18 at 17:01
• @PhilFreedenberg, the diagram has two currents in question--i1 and i. Are they assumed to be equal? – romeoPH Jun 18 at 17:49
• @romeoPH Immediately after the switch is opened, what can you say about i1 and 1? (This is not an assumption; use KCL) – Phil Freedenberg Jun 18 at 23:39