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NEET PHYSICSALTERNATING CURRENTMedium

Question

The potential differences across the resistance, capacitance and inductance are 80 V, 40 V and 100 V respectively in an LCR circuit. What is the power factor of this circuit?

A

0.4

B

0.5

C

0.8

D

1

Step-by-Step Solution

In a series LCR circuit, the total voltage (V) is the phasor sum of the voltages across the components. Since the voltage across the inductor (VLV_L) and the capacitor (VCV_C) are 180∘180^\circ out of phase, the net reactive voltage is VL−VCV_L - V_C (or VC−VLV_C - V_L). The voltage across the resistor (VRV_R) is 90∘90^\circ out of phase with the net reactive voltage. Using the values given: VR=80V_R = 80 V, VC=40V_C = 40 V, VL=100V_L = 100 V. The net supply voltage VV is given by V=VR2+(VL−VC)2=802+(100−40)2=802+602=6400+3600=10000=100V = \sqrt{V_R^2 + (V_L - V_C)^2} = \sqrt{80^2 + (100 - 40)^2} = \sqrt{80^2 + 60^2} = \sqrt{6400 + 3600} = \sqrt{10000} = 100 V. The power factor (cos⁡ϕ\cos \phi) is defined as the ratio of resistance to impedance (R/ZR/Z) or equivalently the ratio of the potential difference across the resistor to the total potential difference (VR/VV_R/V) . Power Factor = VR/V=80/100=0.8V_R / V = 80 / 100 = 0.8.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from ALTERNATING CURRENT. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSALTERNATING CURRENTpotentialdifferencesacrossresistancecapacitance

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