There is 20 volt across the inductor and 15 volt across the resistance in the a.c. supplied series R - L circuit. What would be the supply voltage?a)20 voltb)15 voltc)25 voltd)17.5 voltCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Given information:
- Voltage across the inductor (L): 20 V
- Voltage across the resistance (R): 15 V

To find:
The supply voltage in the series R-L circuit.

Solution:

1. Understanding the series R-L circuit:
In a series R-L circuit, the total voltage (supply voltage) is divided across the inductor and the resistor. The voltage across the inductor leads the current by 90 degrees, while the voltage across the resistor is in phase with the current.

2. Voltage across the inductor:
The voltage across the inductor in an AC circuit can be calculated using the formula V_L = IXL, where V_L is the voltage across the inductor, I is the current flowing through the circuit, and XL is the inductive reactance.

In this case, we are given the voltage across the inductor (V_L) as 20 V. However, we do not have the value of inductive reactance (XL) or the current (I).

3. Voltage across the resistance:
The voltage across the resistor in a series R-L circuit is given by Ohm's law: V_R = IR, where V_R is the voltage across the resistor, I is the current flowing through the circuit, and R is the resistance.

In this case, we are given the voltage across the resistor (V_R) as 15 V. However, we do not have the value of the resistance (R) or the current (I).

4. Relationship between the supply voltage and the voltages across the inductor and resistor:
In a series R-L circuit, the supply voltage (V_s) can be calculated using the Pythagorean theorem: V_s^2 = V_L^2 + V_R^2.

Given that V_L = 20 V and V_R = 15 V, we can substitute these values into the equation:

V_s^2 = (20 V)^2 + (15 V)^2
V_s^2 = 400 V^2 + 225 V^2
V_s^2 = 625 V^2

Taking the square root of both sides, we get:

V_s = 25 V

Therefore, the supply voltage in the given series R-L circuit is 25 volts.

Answer:
The supply voltage is 25 volts (option C).

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