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In a series R-L circuit supplied from a sinusoidal voltage source, voltage across R and L are 3 V and 4 V respectively. The supply voltage is then
- a)7 V
- b)1 V
- c)3.5 V
- d)5 V
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In a series R-L circuit supplied from a sinusoidal voltage source, vol...
Given data,
VR = 3V
VL = 4V
Vs = √(VR2 + VL2)
Vs = √(9+16)
Supply Voltage (Vs) = 5V
VR = 3V
VL = 4V
Vs = √(VR2 + VL2)
Vs = √(9+16)
Supply Voltage (Vs) = 5V
Most Upvoted Answer
In a series R-L circuit supplied from a sinusoidal voltage source, vol...
Calculation of Impedance
The first step in solving this problem is to calculate the impedance of the circuit. Impedance is the total opposition to current flow in an AC circuit and is expressed in ohms. The formula for impedance in an R-L circuit is:
Z = √(R^2 + XL^2)
Where R is the resistance in ohms, XL is the inductive reactance in ohms, and Z is the impedance in ohms.
Given that the voltage across R is 3 V and the current flowing through R is the same as the current flowing through L, we can use Ohm's law to calculate the resistance of the circuit:
R = V/I
Where V is the voltage across R (3 V) and I is the current flowing through the circuit. Since the current flowing through R is the same as the current flowing through L, we can use the voltage across L (4 V) to calculate the inductive reactance:
XL = V/I
Where V is the voltage across L (4 V) and I is the current flowing through the circuit. Substituting the values into the formula for impedance, we get:
Z = √(R^2 + XL^2) = √(3^2 + 4^2) = √25 = 5 ohms
Calculation of Supply Voltage
Once we have calculated the impedance of the circuit, we can use Ohm's law to calculate the supply voltage:
V = IZ
Where V is the supply voltage, I is the current flowing through the circuit, and Z is the impedance of the circuit. Since we know the voltage across R and L, we can use the voltage across R to calculate the current flowing through the circuit:
I = V/R = 3/5 = 0.6 A
Substituting the values into the formula for supply voltage, we get:
V = IZ = 0.6 x 5 = 3 V
Therefore, the correct answer is option D, 5 V.
The first step in solving this problem is to calculate the impedance of the circuit. Impedance is the total opposition to current flow in an AC circuit and is expressed in ohms. The formula for impedance in an R-L circuit is:
Z = √(R^2 + XL^2)
Where R is the resistance in ohms, XL is the inductive reactance in ohms, and Z is the impedance in ohms.
Given that the voltage across R is 3 V and the current flowing through R is the same as the current flowing through L, we can use Ohm's law to calculate the resistance of the circuit:
R = V/I
Where V is the voltage across R (3 V) and I is the current flowing through the circuit. Since the current flowing through R is the same as the current flowing through L, we can use the voltage across L (4 V) to calculate the inductive reactance:
XL = V/I
Where V is the voltage across L (4 V) and I is the current flowing through the circuit. Substituting the values into the formula for impedance, we get:
Z = √(R^2 + XL^2) = √(3^2 + 4^2) = √25 = 5 ohms
Calculation of Supply Voltage
Once we have calculated the impedance of the circuit, we can use Ohm's law to calculate the supply voltage:
V = IZ
Where V is the supply voltage, I is the current flowing through the circuit, and Z is the impedance of the circuit. Since we know the voltage across R and L, we can use the voltage across R to calculate the current flowing through the circuit:
I = V/R = 3/5 = 0.6 A
Substituting the values into the formula for supply voltage, we get:
V = IZ = 0.6 x 5 = 3 V
Therefore, the correct answer is option D, 5 V.
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In a series R-L circuit supplied from a sinusoidal voltage source, voltage across R and L are 3 V and 4 V respectively. The supply voltage is thena)7 Vb)1 Vc)3.5 Vd)5 VCorrect answer is option 'D'. Can you explain this answer?
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