First slide

Electrical Resonance series circuit

Question

What can be said about two series resonant LCR circuits if same current flows through them when connected across a sinusodial voltage source?

Moderate

A

Both the circuits having same value of capacitance and inductance.
B

In both circuits ratio of L and C will be same
C

For both the circuits, X_L / Х_C must be same at that frequency
D

Both the circuits must have same in dependence at all frequencies.

Solution

We are given that the two series LCR circuit are at resonance.
When the circuit is in resonance the value of X_L = X_C.
$i.e., {(X_{L})}_{1} = {(X_{C})}_{1}$
${(X_{L})}_{2} = {(X_{C})}_{2}$
${(\frac{XL}{X_{C}})}_{1} = 1$
${(\frac{X_{L}}{X_{C}})}_{2} = 1$
$\Rightarrow {(\frac{X_{L}}{X_{C}})}_{1} = {(\frac{X_{L}}{X_{C}})}_{2}$
For both the the circuits the ratio
$\frac{X_{L}}{X_{C}} will be same.$

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