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In a series resonant circuit, the A.C. voltages across the resistance R, the inductor L and the capacitor C are 5 V, 10 V and 10 V respectively. The A.C. voltage applied to the circuit will be ______.

Asked in GUJCET 2009 · Current and voltage at resonance

• (1) 25 V
• (2) 20 V
• (3) 10 V
• (4) 5 V

Step-by-step solution

Why the other options are wrong

• (1) 25 V is the plain sum 5+10+10. The three voltages are out of phase with one another, so they add as phasors, not as numbers.
• (2) No single slip gives exactly 20 V. The nearest route, adding V_L and V_C instead of subtracting them, gives √5²+20²=20.6 V; but V_L and V_C are exactly opposite in phase, so they cancel.
• (3) 10 V is V_L (or V_C) alone, read as the supply voltage. At resonance these two are equal and opposite, so together they add nothing to the supply voltage.

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