In this problem, a step voltage of 10 volts is applied to a series RC circuit at T=0 seconds. The initial charge on the capacitor is zero. We need to find the current flowing in the circuit using Laplace transform.


To find the current using Laplace transform, we need to first find the Laplace transform of the voltage and then use it to find the Laplace transform of the current.


To find the Laplace transform of the voltage, we can use the formula:

V(s) = L{v(t)} = L{10u(t)} = 10/s

Where u(t) is the unit step function.


The circuit consists of a resistor and a capacitor in series. The Laplace transform of the current can be found using the formula:

I(s) = V(s)/Z(s)

Where Z(s) is the impedance of the circuit.

The impedance of a series RC circuit is given by:

Z(s) = R + 1/(sC)

Substituting the values of R and C, we get:

Z(s) = 1 + 1/(sC)

Therefore, the Laplace transform of the current is:

I(s) = V(s)/Z(s) = 10/s * 1/(1 + sRC)


To find the time-domain current, we need to take the inverse Laplace transform of I(s). The inverse Laplace transform of 1/(1 + sRC) is given by:

L^-1{1/(1 + sRC)} = e^(-t/RC)

Therefore, the time-domain current is given by:

i(t) = L^-1{I(s)} = 10*e^(-t/RC)


In this problem, we used Laplace transform to find the current flowing in a series RC circuit when a step voltage is applied. The Laplace transform of the voltage was found to be 10/s and the Laplace transform of the current was found to be 10*e^(-t/RC)/(1 + sRC). Taking the inverse Laplace transform of the current, we get the time-domain current as 10*e^(-t/RC).