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In a series LCR a.c. circuit the voltage across each of L, C and R is 50 V. The voltage across the L-C combination is

Asked in AIEEE 2004 · Voltages across the elements

(1) 50 V
(2) 50√2 V
(3) 100 V
(4) 0 V (zero)

Answer: (4) 0 V (zero)

Step-by-step solution

V_L and V_C are 180° out of phase, so across the L-C combination they subtract.

V_LC=|V_L-V_C|=|50-50|=0 V.

Why the other options are wrong

(1) Takes just one of the two voltages.
(2) Combines them as if 90° apart.
(3) Adds V_L and V_C in phase, ignoring that they oppose.

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