In an LCR series circuit, source of emf is :
$E=30 \sin (100t)$ and $R= 120, L=100 mH, C= 100 μF$
(A) The numerical value of impedance
(B) The numerical value of Resistance R
(C) The numerical value of capacitive reactance
(D) The numerical value of inductive reactance
Arrange the values of quantities mentioned in (A, B, C, D) in increasing order.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (D), (C), (B), (A)
The impedance (Z) is,
$Z=\sqrt{R^2+(X_L-X_C)^2}$
$=\sqrt{120^2+(100×0.1-\frac{1}{100×100×10^{-6}})^2}$
$=\sqrt{120^2+90^2}=\sqrt{22500}$
$=150Ω$
and,
$X_L=ωL=100×0.1=10Ω$
$X_C=\frac{1}{ωC}=\frac{1}{100×100×10^{-6}}=100Ω$
$∴X_L<X_C<R<Z$