homework regarding RLC circuit

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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??:confused:
 

steveb

Joined Jul 3, 2008
2,431
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??:confused:
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.
 
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