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A coil has resistance 30 ohm and inductive reactance 20 ohm at 50 Hz frequency. If an ac source, of 200 volt, 100 Hz, is connected across the coil, the current in the coil will be
- a)4.0 A
- b)8.0 A
- c)7.2 A
- d)2.0 A
Correct answer is option 'A'. Can you explain this answer?
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A coil has resistance 30 ohm and inductive reactance 20 ohm at 50 Hz f...
If ω = 50 × 2π then wL = 20Ω If ω' = 100 × 2π then ω'L = 40Ω Current flowing in the coil is
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A coil has resistance 30 ohm and inductive reactance 20 ohm at 50 Hz f...
The given problem involves a coil with resistance and inductive reactance connected to an AC source. We are asked to determine the current in the coil when a 200 V, 100 Hz AC source is connected.
Given data:
Resistance of the coil (R) = 30 ohm
Inductive reactance of the coil (XL) = 20 ohm
Frequency of the AC source (f) = 100 Hz
Voltage of the AC source (V) = 200 V
To find the current in the coil, we need to calculate the impedance (Z) of the coil using the resistance and inductive reactance. The impedance is given by the formula:
Z = √(R² + XL²)
Impedance (Z) = √(30² + 20²) = √(900 + 400) = √1300 = 36.06 ohm (approx.)
The impedance (Z) represents the total opposition to the flow of current in an AC circuit, combining both resistance and reactance.
Now, we can use Ohm's Law to calculate the current (I) in the coil. Ohm's Law states that:
I = V / Z
Current (I) = 200 V / 36.06 ohm = 5.54 A (approx.)
However, we need to remember that the inductive reactance (XL) is dependent on the frequency (f) of the AC source. In this problem, the given frequency is 100 Hz, but the reactance value is given at 50 Hz. To adjust for the difference in frequency, we need to use the formula:
XL = 2πfL
Where L is the inductance of the coil. Since the inductance is not given, we cannot calculate the exact value of XL. However, we can assume that the inductive reactance at 100 Hz would be approximately double the reactance at 50 Hz.
So, the adjusted inductive reactance at 100 Hz would be 2 * 20 ohm = 40 ohm.
Now, we can recalculate the impedance (Z) using the adjusted reactance value:
Z = √(R² + XL²) = √(30² + 40²) = √(900 + 1600) = √2500 = 50 ohm (approx.)
Using Ohm's Law, the current (I) in the coil would be:
I = V / Z = 200 V / 50 ohm = 4 A
Therefore, the correct answer is option A - the current in the coil will be 4.0 A.
Given data:
Resistance of the coil (R) = 30 ohm
Inductive reactance of the coil (XL) = 20 ohm
Frequency of the AC source (f) = 100 Hz
Voltage of the AC source (V) = 200 V
To find the current in the coil, we need to calculate the impedance (Z) of the coil using the resistance and inductive reactance. The impedance is given by the formula:
Z = √(R² + XL²)
Impedance (Z) = √(30² + 20²) = √(900 + 400) = √1300 = 36.06 ohm (approx.)
The impedance (Z) represents the total opposition to the flow of current in an AC circuit, combining both resistance and reactance.
Now, we can use Ohm's Law to calculate the current (I) in the coil. Ohm's Law states that:
I = V / Z
Current (I) = 200 V / 36.06 ohm = 5.54 A (approx.)
However, we need to remember that the inductive reactance (XL) is dependent on the frequency (f) of the AC source. In this problem, the given frequency is 100 Hz, but the reactance value is given at 50 Hz. To adjust for the difference in frequency, we need to use the formula:
XL = 2πfL
Where L is the inductance of the coil. Since the inductance is not given, we cannot calculate the exact value of XL. However, we can assume that the inductive reactance at 100 Hz would be approximately double the reactance at 50 Hz.
So, the adjusted inductive reactance at 100 Hz would be 2 * 20 ohm = 40 ohm.
Now, we can recalculate the impedance (Z) using the adjusted reactance value:
Z = √(R² + XL²) = √(30² + 40²) = √(900 + 1600) = √2500 = 50 ohm (approx.)
Using Ohm's Law, the current (I) in the coil would be:
I = V / Z = 200 V / 50 ohm = 4 A
Therefore, the correct answer is option A - the current in the coil will be 4.0 A.
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A coil has resistance 30 ohm and inductive reactance 20 ohm at 50 Hz frequency. If an ac source, of 200 volt, 100 Hz, is connected across the coil, the current in the coil will bea)4.0 Ab)8.0 Ac)7.2 Ad)2.0 ACorrect answer is option 'A'. Can you explain this answer?
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A coil has resistance 30 ohm and inductive reactance 20 ohm at 50 Hz frequency. If an ac source, of 200 volt, 100 Hz, is connected across the coil, the current in the coil will bea)4.0 Ab)8.0 Ac)7.2 Ad)2.0 ACorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A coil has resistance 30 ohm and inductive reactance 20 ohm at 50 Hz frequency. If an ac source, of 200 volt, 100 Hz, is connected across the coil, the current in the coil will bea)4.0 Ab)8.0 Ac)7.2 Ad)2.0 ACorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A coil has resistance 30 ohm and inductive reactance 20 ohm at 50 Hz frequency. If an ac source, of 200 volt, 100 Hz, is connected across the coil, the current in the coil will bea)4.0 Ab)8.0 Ac)7.2 Ad)2.0 ACorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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