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Question

A pure resistance R, pure capacitance C and pure inductance L are connected in series and the impedance of the circuit at resonance is Z0. If they are connected in parallel to each other, the maximum impedance at resonance will be:


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Solution

Step 1: Given

The resistance of the resistor is R.

The capacitance of the capacitor is C.

The Inductance of the inductor is L.

Step 2: Formulas used

Impedance (Z) is the opposition offered to the flow of current in a circuit. Its magnitude is given as,
Z=R2+X2
where, R is the resistance offered by the resistor and X is the reactance.

Reactance is a measure of how much electrical energy is stored or released in the circuit.
It is caused by the current being out of phase from the electromotive force causing it. It is given as
X=XL-XC
where, XL is the inductive reactance and XC is the capacitive reactance.

Step 3: Calculate the maximum impedance at resonance when in parallel

When in parallel, at resonance,
XL=XC

Thus, overall reactance is,
X=XL-XCX=XL-XLXL=XCX=0

Thus, the magnitude of impedance will be,
Z=R2+02Z=R2Z=R

Therefore, when a pure RLC circuit is in parallel, the maximum impedance at resonance is the resistance of the resistor R.


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