# homework regarding RLC circuit

#### Hanck

Joined Nov 25, 2008
18
A circuit has 2 parallel branches with a parallel ac voltage source. One branch consists of 1 R and 1 C and another branch has 1 R and 1 L. The component value are such that L = C(R^2).

The problem is how do i show that the impedance of the circuit is constant at all frequency and the supply current and voltage are in phase??

#### steveb

Joined Jul 3, 2008
2,436
A circuit has 2 parallel branches with a parallel ac voltage source. One branch consists of 1 R and 1 C and another branch has 1 R and 1 L. The component value are such that L = C(R^2).

The problem is how do i show that the impedance of the circuit is constant at all frequency and the supply current and voltage are in phase??
Write the equivalent impedance in the frequency domain using Laplace transform.

XL=sL=sCR^2
XC=1/(sC)

Use the product over sum formula to express impedance of a parallel combination. Then simplify the math. The result will be a real number independent of frequency (s), which implies a resistive load on the AC source.