Question

The correct formula for electric power in an electric circuit is:

• A. \( P = iR \)
• B. \( P = i^2R \)
• C. \( P = \frac{V^2}{R} \)
• D. \( P = iR^2 \)

Hint:

Use \( P = VI \), \( P = I^2R \), or \( P = \frac{V^2}{R} \) depending on what's given in the problem (voltage, current, or resistance).

Answer 1

The Correct Option is B

The electric power \( P \) consumed in an electrical circuit refers to the rate at which electrical energy is converted into other forms of energy such as heat, light, or mechanical work. The expression for electric power can take different forms depending on the quantities available: \[ P = VI, \quad P = I^2R, \quad \text{or} \quad P = \frac{V^2}{R} \] These three equations are derived from
Ohm’s Law, which states that \( V = IR \),
where:


\( V \) is the potential difference (voltage),
\( I \) is the current,
\( R \) is the resistance.
\smallskip 1.
First Formula: \( P = VI \)
This is the basic definition of electric power — the product of voltage and current. It is used when both voltage across and current through a component are known. \smallskip 2.
Second Formula: \( P = I^2R \)
By substituting \( V = IR \) into the power formula \( P = VI \), we get: \[ P = I(IR) = I^2R \] This expression is useful when current and resistance are known. It shows that power is directly proportional to the square of the current, making it particularly important in analyzing energy loss due to resistance (e.g., in transmission lines). \smallskip 3.
Third Formula: \( P = \frac{V^2}{R} \)
Similarly, by substituting \( I = \frac{V}{R} \) into \( P = VI \), we get: \[ P = V\left( \frac{V}{R} \right) = \frac{V^2}{R} \] This form is used when voltage and resistance are known. \smallskip In the given question, option (b) \( P = I^2R \) is correct. It is one of the standard and widely used formulas for calculating electric power, especially when current and resistance are the known quantities.