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A resistance of 7 ohm is connected in series with an inductance of 31.8mH. The circuit is connected to a x V 50Hz sinusoidal supply. The current in the circuit is 8.2A. Calculate the value of x.
- a)10V
- b)50V
- c)100V
- d)120V
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A resistance of 7 ohm is connected in series with an inductance of 31....
XL=2*pi*f*L= 10ohm. Therefore the total impedance =sqrt(R2+XL2)=12.2ohm.
V=IZ, Therefore V=12.2*8.2=100V.
V=IZ, Therefore V=12.2*8.2=100V.
Most Upvoted Answer
A resistance of 7 ohm is connected in series with an inductance of 31....
To solve this problem, we can use the concept of impedance in an AC circuit. Impedance is the effective resistance to the flow of alternating current in a circuit that contains both resistive and reactive components. In this case, the inductance is the reactive component.
1. Impedance calculation:
The impedance (Z) of the circuit can be calculated using the formula:
Z = √(R^2 + (XL - XC)^2)
where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance (which is zero in this case since there is no capacitance).
Given:
Resistance (R) = 7 ohm
Inductance (L) = 31.8mH = 0.0318 H
Frequency (f) = 50 Hz
The inductive reactance (XL) can be calculated using the formula:
XL = 2πfL
Plugging in the values:
XL = 2π × 50 × 0.0318 = 9.999 ohm (approximately 10 ohm)
Now we can calculate the impedance:
Z = √(7^2 + (10 - 0)^2) = √(49 + 100) = √149 ≈ 12.206 ohm
2. Voltage calculation:
The voltage (V) across the circuit can be calculated using Ohm's law:
V = I × Z
where I is the current and Z is the impedance.
Given:
Current (I) = 8.2 A
Impedance (Z) = 12.206 ohm
Plugging in the values:
V = 8.2 × 12.206 ≈ 100.064 V (approximately 100 V)
Therefore, the value of x is approximately 100V, which corresponds to option (c) in the provided choices.
1. Impedance calculation:
The impedance (Z) of the circuit can be calculated using the formula:
Z = √(R^2 + (XL - XC)^2)
where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance (which is zero in this case since there is no capacitance).
Given:
Resistance (R) = 7 ohm
Inductance (L) = 31.8mH = 0.0318 H
Frequency (f) = 50 Hz
The inductive reactance (XL) can be calculated using the formula:
XL = 2πfL
Plugging in the values:
XL = 2π × 50 × 0.0318 = 9.999 ohm (approximately 10 ohm)
Now we can calculate the impedance:
Z = √(7^2 + (10 - 0)^2) = √(49 + 100) = √149 ≈ 12.206 ohm
2. Voltage calculation:
The voltage (V) across the circuit can be calculated using Ohm's law:
V = I × Z
where I is the current and Z is the impedance.
Given:
Current (I) = 8.2 A
Impedance (Z) = 12.206 ohm
Plugging in the values:
V = 8.2 × 12.206 ≈ 100.064 V (approximately 100 V)
Therefore, the value of x is approximately 100V, which corresponds to option (c) in the provided choices.
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A resistance of 7 ohm is connected in series with an inductance of 31.8mH. The circuit is connected to a x V 50Hz sinusoidal supply. The current in the circuit is 8.2A. Calculate the value of x.a)10Vb)50Vc)100Vd)120VCorrect answer is option 'C'. Can you explain this answer?
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