Question 9: AC fundamentals

Question

A resistance $$R$$ and inductance $$L$$ and a capacitor $$C$$ all are connected in series with an $$\mathrm{AC}$$ supply. The resistance of $$R$$ is $$24 \mathrm{~ohm}$$ and for a given frequency, the inductive reactance of $$L$$ is 36 ohm and capacitive reactance of $$C$$ is $$24 \mathrm{~ohm}$$. If the current in the circuit is $$5 \mathrm{~amp}$$. Find the potential difference across $$R, L$$ and $$C$$.

Accepted Answer

To determine the potential differences across the resistor $$R$$, inductor $$L$$, and capacitor $$C$$ in a series AC circuit, we can use Ohm's Law and the given impedances.
Given:
$$R = 24 	extrm{ ohm}$$
Inductive reactance $$X_L = 36 	extrm{ ohm}$$
Capacitive reactance $$X_C = 24 	extrm{ ohm}$$
Current in the circuit $$I = 5 	extrm{ amp}$$
First, we find the potential difference across each component using Ohm's Law:
Potential difference across $$R$$:
$$ V_R = I \cdot R $$
$$ V_R = 5 	extrm{ amp} \cdot 24 	extrm{ ohm} $$
$$ V_R = 120 	extrm{ V} $$
Potential difference across $$L$$:
$$ V_L = I \cdot X_L $$
$$ V_L = 5 	extrm{ amp} \cdot 36 	extrm{ ohm} $$
$$ V_L = 180 	extrm{ V} $$
Potential difference across $$C$$:
$$ V_C = I \cdot X_C $$
$$ V_C = 5 	extrm{ amp} \cdot 24 	extrm{ ohm} $$
$$ V_C = 120 	extrm{ V} $$
Summarizing, the potential differences are:
$$V_R = 120 	extrm{ V}$$
$$V_L = 180 	extrm{ V}$$
$$V_C = 120 	extrm{ V}$$
Therefore, the correct answer is:
Option D: $$120, 180, 120 	extrm{ V}$$

Answer

$$140,140,120 \mathrm{~V}$$

Answer

$$80,120,120 \mathrm{~V}$$

Answer

$$140,140,120 \mathrm{~V}$$

Answer

$$120,180,120 \mathrm{~V}$$

AC fundamentals

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