In given circuit R = 100 Ω . If voltage leads current by 60 ∘ then find average power.

The voltage across the circuit V = 200 sin 100 π t V and voltage leads the current, current lags by 60 ° . According to the phasor diagram, the phase angle tan ϕ = X L - X C R ⇒ tan 60 ° = X L - X C 100 ⇒ X L - X C = 100 3 Ω The impedance of the circuit Z = R 2 + ( X L - X C ) 2 ⇒ Z = ( 100 ) 2 + ( 100 2 ) 2 ⇒ Z = 200 Ω , The peak voltage V 0 = 200 V , The RMS voltage E RMS = V 0 2 = 200 2 = 100 2 V , The RMS current I RMS = V RMS Z According to the Phasor diagram, Power factor cos ϕ = R Z ⇒ cos ϕ = 100 200 = 1 2 Average Power P avg = E RMS I RMS cos ϕ ⇒ P avg = E RMS 2 Z cos ϕ ⇒ P avg = ( 100 2 ) 2 200 × 1 2 ⇒ P avg = 50 W

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Beta Question Bank for Medical: Physics>Chapter 28 - Alternating Current>Exercise (Conceptual Questions)>Q 13

In given circuit $R = 100 Ω$ . If voltage leads current by $60^{\circ}$ then find average power.

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