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Question: In a series resonant circuit, the AC voltage across resistance R, inductor L and capacitor C, are \(...

In a series resonant circuit, the AC voltage across resistance R, inductor L and capacitor C, are 5 V5\,V ,10  V10\,\,V and 10 V10\,V respectively. The AC voltage applied to the circuit will be
A.10 V10\,V
B. 25  V25\,\,V
C.5 V5\,V
D.20 V20\,V

Explanation

Solution

Hint- A series LCR circuit also known as resonant circuit is a circuit in which the inductor capacitor and resistor are connected in series.
The AC voltage applied to the series resonant circuit is given as
V=VR2+(VL−VC)2V = \sqrt {{V_R}^2 + {{({V_L} - {V_C})}^2}}
VR{V_R} is the voltage across the resistor, VL{V_L} is the voltage across the inductor and VC{V_C} is the voltage across the capacitor.

Step by step solution:
A series LCR circuit also known as resonant circuit is a circuit in which the inductor capacitor and resistor are connected in series
Resonance in series circuits is the phenomenon in which the output of a circuit is maximum at one particular frequency and that particular frequency is known as the resonant frequency. At the resonant frequency the capacitive reactance and inductive reactance are equal
Given,
Voltage across resistor, VR= 5 V{V_R} = \,5\,V
Voltage across inductor, VL=10 V{V_L} = 10\,V
Voltage across capacitor, VC=10 V{V_C} = 10\,V
the AC voltage applied to the circuit is given as
V=VR2+(VL−VC)2V = \sqrt {{V_R}^2 + {{({V_L} - {V_C})}^2}}
Substituting the given values, we get,

V=VR2+(VL−VC)2 =(5)2+(10−10)2 =5 V  V = \sqrt {{V_R}^2 + {{({V_L} - {V_C})}^2}} \\\ = \sqrt {{{(5)}^2} + {{(10 - 10)}^2}} \\\ = 5\,V \\\

So, option C is correct

Additional information: Series resonant circuit is one of the most important circuits used in electrical devices They are used in various forms such as in AC main filters, noise filters, radio and television tuning circuits for selective tuning and receiving of the different frequency channels.

Note: In a series resonance circuit current through the resistor inductor and capacitor will be the same. But the voltage drop across the resistor inductor and capacitor will be different. In the case of a parallel resonance circuit voltage across the resistor inductor and capacitor will be the same. But current flowing will be different in each of them.