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In a series L-R circuit, connected with ...

In a series `L-R` circuit, connected with a sinusoidal ac source, the maximum potential difference acrosssd `L` and `R` are respectively 3 volts and 4 volts
At the same instant, the magnitude of the potential difference in volt, across the ac source will be

A

`3 cos 67^(@)`

B

`5 sin 37^(@)`

C

`6 cos 97^(@)`

D

0

Text Solution

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The correct Answer is:
To find the magnitude of the potential difference across the AC source in a series L-R circuit, we can use the relationship between the voltages across the resistor (R) and inductor (L). The voltages across these components can be represented as phasors, and we can apply the Pythagorean theorem to find the total voltage across the source. ### Step-by-Step Solution: 1. **Identify the Maximum Voltages**: - The maximum potential difference across the inductor (L) is given as \( V_L = 3 \) volts. - The maximum potential difference across the resistor (R) is given as \( V_R = 4 \) volts. 2. **Use the Pythagorean Theorem**: - In a series L-R circuit, the total voltage across the AC source (\( V_{AC} \)) can be calculated using the formula: \[ V_{AC} = \sqrt{V_R^2 + V_L^2} \] - Substitute the values: \[ V_{AC} = \sqrt{(4)^2 + (3)^2} \] - Calculate the squares: \[ V_{AC} = \sqrt{16 + 9} \] - Add the squares: \[ V_{AC} = \sqrt{25} \] - Take the square root: \[ V_{AC} = 5 \text{ volts} \] 3. **Conclusion**: - The magnitude of the potential difference across the AC source is \( 5 \) volts.
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