What is the voltage across the capacitor when the source voltage is 10...
We know that voltage across the capacitor in resonance condition is equal to Q times the source voltage =10*100=1000V.
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What is the voltage across the capacitor when the source voltage is 10...
Explanation:
To understand the voltage across the capacitor, we need to consider the concept of the Q factor and its relationship with the voltage and impedance of a circuit.
Q factor:
The Q factor, also known as the quality factor, is a dimensionless parameter that describes the behavior of a resonant circuit. It is defined as the ratio of the reactance to the resistance in the circuit.
Resonant circuit:
A resonant circuit consists of an inductor and a capacitor connected in series or parallel. The circuit exhibits resonance at a specific frequency, where the reactances of the inductor and capacitor cancel each other out, resulting in a purely resistive impedance.
Voltage across the capacitor:
In a series resonant circuit, the voltage across the capacitor is maximum at resonance. This is because the capacitive reactance is equal to the inductive reactance, resulting in a cancellation of reactances and leaving only the resistance.
Given values:
Source voltage (Vs) = 100V
Q factor = 10
Calculation:
To find the voltage across the capacitor, we need to calculate the impedance of the circuit and then determine the voltage drop across the capacitor.
Impedance of the circuit:
The impedance of a series resonant circuit is given by the following equation:
Z = √(R^2 + (XL - XC)^2)
Where:
Z = Impedance of the circuit
R = Resistance of the circuit
XL = Inductive reactance
XC = Capacitive reactance
At resonance, XL = XC, so the equation simplifies to:
Z = √(R^2)
Since the Q factor is a ratio of reactance to resistance, we can rewrite the equation as:
Z = R/Q
Voltage across the capacitor:
The voltage across the capacitor (Vc) can be calculated using Ohm's law:
Vc = Vs * (XC / Z)
At resonance, XC = XL and Z = R/Q, so the equation simplifies to:
Vc = Vs * (XL / (R/Q))
Vc = Vs * (XL * Q / R)
Substituting the given values:
Vs = 100V
Q = 10
Vc = 100V * (XL * 10 / R)
Since the Q factor and the resistance are not given, we cannot determine the exact voltage across the capacitor. Therefore, the correct answer cannot be determined from the given information.
So, the correct answer is not provided in the options given.