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प्रश्न
Choose the correct option.
In a circuit L, C and R are connected in series with an alternating voltage of frequency f. the current leads the voltage by 45°. The value of C is ______.
पर्याय
`1/(πf(2πfL - R))`
`1/(2πf(2πfL - R))`
`1/(πf(2πfL + R))`
`1/(2πf(2πfL + R))`
उत्तर
In a circuit L, C and R are connected in series with an alternating voltage of frequency f. the current leads the voltage by 45°. The value of C is `1/(2πf(2πfL - R))`.
Explanation:
Let, Inductance = L
Conductance = C
Resistance = R
Frequency = f
Phase Difference between current and voltage =
∴ `tan phi = (X_L - X_C)/R` ......(1)
The current leads the voltage by 45°
Therefore, `phi` = 45°
`tan phi` = tan 45° = 1 .....(2)
Put the values in equation (1) and (2) and calculate:
∴ `(X_L - X_C)/R` = 1
`X_C = X_L - R`
`1/(2pifC) = 2pifL - R`
C = `1/(2pif(2pifL - R))`
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