MHT CET20225 Aug 2022Morning ShiftPhysicsAlternating CurrentActual
With an alternating voltage source of frequency ' f ', inductor ' L ', capacitor ' C ' and resistance ' R ' are connected in series. The voltage leads the currently by 45^ . The value of ' L ' is ( . 45^ =1 )
Options
- A( 4 ^2 f^2 C 1+2 f C R )
- B( 1+2 fCR 4 ^2 f ^2 C )
- C( 1-2 fCR 4 ^2 f ^2 C )
- D( 4 ^2 f^2 C 1-2 f C R )
Correct answer
B. ( 1+2 fCR 4 ^2 f ^2 C )
Step-by-step solution
The correct option is (B). Concept: Consider the following Phasor diagram for a series LCR circuit: If the voltage leads the current by an angle =45^ then, aligned & ( )= (X_L-X_C ) R = (45^ ) & X_L-X_C=R aligned Introducing, inductive reactance X_L=2 fL , capacitive reactance X_C= 1 2 f C and resistor R2 f L- 1 2 f C =R On re-writing, L= ( 1 2 f C +R ) ( 1 2 f ) or ( 1+2 f C R 4 ^2 f^2 C )