2R-1C Combination Step Input Voltage Response | RC Circuit Analog Interview Questions

In my previous post RC Circuit Analysis , I have described the fundamentals of simple Analog RC circuit which is the backbone of all other RC circuit combination analysis. I highly recommend to go through the previous post RC Circuit Analysis to get familiarize with fundamentals of RC analysis.

In this post we are going discuss the behaviour of 2R-1C RC circuit excited with step voltage input. In our analysis all the components are considered ideal.

The 2R-1C combination RC circuit is given below.

From our earlier analysis in RC Circuit Analysis , we are aware that we need to find out the voltage across capacitor and current flowing through it at time t=0+ and t=infinity.

Analysis at time t=0+

Now, for the above circuit, before application of input voltage capacitors is fully discharged (voltage across it = 0 v). After application of step voltage, from the fundamental property of capacitors, the capacitor will prevent the sudden change of the voltage across it and will try to remain at voltage=0.

From our previous analysis, at $t=0+$ the circuit will look like below.

In the above circuit, we can see capacitor is behaving like a short circuit. This gives us the voltage across capacitor at $t=0+$ is zero. So, the current that flows through the circuit is $i(t=0+)=\frac{V1}{R1}$ . The voltage across resistor $R1, V_R1$ , is same as input voltage $V1$ .

Analysis at time t=infinity

From our previous post with 1R-1C circuit, we know that when capacitor is fully charged it acts like an open circuit and no current flows through it. Keeping this in mind, at t=infinity, let’s say capacitor $C2$ charges fully, behaves as an open circuit and current flowing through is zero. The circuit becomes a series combination of two resistors and input voltage source at t=infinity.