Question

The electrical power of an electrical appliance cannot be expressed by,

• A. VI
• B. I²R
• C. I²/R
• D. V²/R

Answer 1

The correct option is C

I²/R

Concept used: Electrical power

Prerequisite: Knowledge of formulas of electrical power

Step 1: Power in terms of potential and current,

The power supplied by a battery is product of voltage of the battery and current supplied by the battery. Mathematically, it can be written as,

$P=VI......\left(1\right)$

Here, P is the power, V is the voltage, and I is the current.

Step 2: Power in terms of current and resistance,

The expression for the voltage according to Ohm's law is,

$$\begin{gathered} V=IR......\left(2\right) \\ I=\frac{V}{R}......\left(3\right) \end{gathered}$$

Here, R is the resistance.

The power by substituting the expression of equation (2) in equation (1) can also be written as,

$$\begin{gathered} P=VI \\ P=\left(IR\right)R \\ P=I^{2}R \end{gathered}$$

Step 3: Power in terms of potential and resistance,

The power by substituting the expression of equation (3) in equation (1) can also be written as,

$\begin{array}{rcl}P& =& VI\\ P& =& V\left(\frac{V}{R}\right)\\ P& =& \frac{V^2}{R}\end{array}$

Therefore, the expressions for the power are,

$$\begin{gathered} P=VI \\ P=I^{2}R \\ P=\frac{V^2}{R} \end{gathered}$$

Thus, option (c) is correct.