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When V=100Sinwt is applied across a series (R-L-C) circuit, at resonance the current in resistance (R = 100 ohm) is i = i(o)sinwt, then power dissipated in the circuit is A) 50W B) 100W C) 25W D) can't be calculated?
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When V=100Sinwt is applied across a series (R-L-C) circuit, at resonan...
**Resonance in an R-L-C Circuit**
In an R-L-C circuit, resonance occurs when the inductive reactance (XL) and capacitive reactance (XC) are equal, resulting in the circuit's impedance being purely resistive. At resonance, the circuit is highly efficient, and the current flowing through the circuit reaches its maximum value.
**Given Parameters**
- Voltage across the circuit V = 100Sinwt
- Resistance R = 100 ohm
**Calculating the Current**
To find the current flowing through the circuit, we can use Ohm's law, which states that the current (I) is equal to the voltage (V) divided by the impedance (Z).
At resonance, the impedance (Z) is equal to the resistance (R) since XC = XL.
So, Z = R = 100 ohm.
Therefore, the current (I) is given by:
I = V / Z
= V / R
= 100Sinwt / 100
= Sinwt
**Power Dissipation in the Circuit**
The power dissipated in a circuit can be calculated using the formula P = I^2 * R, where P is the power, I is the current, and R is the resistance.
Substituting the value of current (I) in the formula:
P = (Sinwt)^2 * R
= (Sin^2 wt) * R
= (1/2 - (1/2)Cos2wt) * R
= (1/2) * R - (1/2)Cos2wt * R
Since the average value of Cos2wt over a complete cycle is zero, the average power dissipated in the circuit is given by:
Average P = (1/2) * R
= (1/2) * 100
= 50W
**Answer**
The power dissipated in the circuit at resonance is 50W (Option A).
**Explanation**
At resonance, the current in the circuit is maximum, resulting in increased power dissipation. The power dissipated can be calculated using the formula P = I^2 * R, where I is the current and R is the resistance. By substituting the value of current, we find that the average power dissipated in the circuit is 50W. Therefore, the correct answer is option A, 50W.
In an R-L-C circuit, resonance occurs when the inductive reactance (XL) and capacitive reactance (XC) are equal, resulting in the circuit's impedance being purely resistive. At resonance, the circuit is highly efficient, and the current flowing through the circuit reaches its maximum value.
**Given Parameters**
- Voltage across the circuit V = 100Sinwt
- Resistance R = 100 ohm
**Calculating the Current**
To find the current flowing through the circuit, we can use Ohm's law, which states that the current (I) is equal to the voltage (V) divided by the impedance (Z).
At resonance, the impedance (Z) is equal to the resistance (R) since XC = XL.
So, Z = R = 100 ohm.
Therefore, the current (I) is given by:
I = V / Z
= V / R
= 100Sinwt / 100
= Sinwt
**Power Dissipation in the Circuit**
The power dissipated in a circuit can be calculated using the formula P = I^2 * R, where P is the power, I is the current, and R is the resistance.
Substituting the value of current (I) in the formula:
P = (Sinwt)^2 * R
= (Sin^2 wt) * R
= (1/2 - (1/2)Cos2wt) * R
= (1/2) * R - (1/2)Cos2wt * R
Since the average value of Cos2wt over a complete cycle is zero, the average power dissipated in the circuit is given by:
Average P = (1/2) * R
= (1/2) * 100
= 50W
**Answer**
The power dissipated in the circuit at resonance is 50W (Option A).
**Explanation**
At resonance, the current in the circuit is maximum, resulting in increased power dissipation. The power dissipated can be calculated using the formula P = I^2 * R, where I is the current and R is the resistance. By substituting the value of current, we find that the average power dissipated in the circuit is 50W. Therefore, the correct answer is option A, 50W.
Community Answer
When V=100Sinwt is applied across a series (R-L-C) circuit, at resonan...
Vrms = V/root 2 = 100 / root 2
power = V^2 /R = [100/root 2] ^2 / 100 = 50 watt
power = V^2 /R = [100/root 2] ^2 / 100 = 50 watt
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When V=100Sinwt is applied across a series (R-L-C) circuit, at resonance the current in resistance (R = 100 ohm) is i = i(o)sinwt, then power dissipated in the circuit is A) 50W B) 100W C) 25W D) can't be calculated?
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When V=100Sinwt is applied across a series (R-L-C) circuit, at resonance the current in resistance (R = 100 ohm) is i = i(o)sinwt, then power dissipated in the circuit is A) 50W B) 100W C) 25W D) can't be calculated? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about When V=100Sinwt is applied across a series (R-L-C) circuit, at resonance the current in resistance (R = 100 ohm) is i = i(o)sinwt, then power dissipated in the circuit is A) 50W B) 100W C) 25W D) can't be calculated? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When V=100Sinwt is applied across a series (R-L-C) circuit, at resonance the current in resistance (R = 100 ohm) is i = i(o)sinwt, then power dissipated in the circuit is A) 50W B) 100W C) 25W D) can't be calculated?.
When V=100Sinwt is applied across a series (R-L-C) circuit, at resonance the current in resistance (R = 100 ohm) is i = i(o)sinwt, then power dissipated in the circuit is A) 50W B) 100W C) 25W D) can't be calculated? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about When V=100Sinwt is applied across a series (R-L-C) circuit, at resonance the current in resistance (R = 100 ohm) is i = i(o)sinwt, then power dissipated in the circuit is A) 50W B) 100W C) 25W D) can't be calculated? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When V=100Sinwt is applied across a series (R-L-C) circuit, at resonance the current in resistance (R = 100 ohm) is i = i(o)sinwt, then power dissipated in the circuit is A) 50W B) 100W C) 25W D) can't be calculated?.
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