Statement I: In an LCR series circuit, current is maximum at resonance.

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Q.
Given below are two statements:

Statement I: In an LCR series circuit, current is maximum at resonance.

Statement II: Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source.

In the light of the above statements, choose the correct from the options given below: [2024]

1 Statement I is true but Statement II is false

2 Statement I is false but Statement II is true

3 Both Statement I and Statement II are false

4 Both Statement I and Statement II are true

Ans.
(4)

Statement-I

   $I_{m} = \frac{V_{m}}{\sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}}, at resonance X_{L} = X_{C}$

   $Thus, I_{m} = \frac{V_{m}}{R}$

   $∴$ Impendence is minimum therefore $I$ is maximum at resonance.

  Statement-II

   $I = (\frac{V}{R}) in purely resistive circuit .$

Solution

1 Statement I is true but Statement II is false

2 Statement I is false but Statement II is true

3 Both Statement I and Statement II are false

4 Both Statement I and Statement II are true

Ans.
(4)

Statement-I

   $I_{m} = \frac{V_{m}}{\sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}}, at resonance X_{L} = X_{C}$

   $Thus, I_{m} = \frac{V_{m}}{R}$

   $∴$ Impendence is minimum therefore $I$ is maximum at resonance.

  Statement-II

   $I = (\frac{V}{R}) in purely resistive circuit .$

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Solution

1 Statement I is true but Statement II is false

2 Statement I is false but Statement II is true

3 Both Statement I and Statement II are false

4 Both Statement I and Statement II are true

Ans. (4) Statement-I Im=VmR2+(XL-XC)2, at resonance XL=XC Thus, Im=VmR ∴ Impendence is minimum therefore I is maximum at resonance. Statement-II I=(VR) in purely resistive circuit.

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Ans.
(4)

Statement-I

$I_{m} = \frac{V_{m}}{\sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}}, at resonance X_{L} = X_{C}$

$Thus, I_{m} = \frac{V_{m}}{R}$

$∴$ Impendence is minimum therefore $I$ is maximum at resonance.

Statement-II

$I = (\frac{V}{R}) in purely resistive circuit .$