Question

Define electric power and derive the relation \(P = VI\).

Hint:

Other forms of electric power are: \[ P = I^2R \quad \text{and} \quad P = \frac{V^2}{R} \]

Answer 1

Concept: Electric power represents the rate at which electrical energy is converted into other forms of energy such as heat, light, or mechanical energy in an electric circuit.
Step 1:Definition of Electric Power} Electric power is defined as the rate at which electrical energy is consumed or used in a circuit. \[ P = \frac{W}{t} \] where \(P\) = electric power
\(W\) = electrical work or energy
\(t\) = time
Step 2:Relation between electrical work and potential difference} Electrical work done in moving a charge \(Q\) through a potential difference \(V\) is given by: \[ W = VQ \] Substituting this in the power equation: \[ P = \frac{VQ}{t} \]
Step 3:Using the definition of current} Electric current is defined as: \[ I = \frac{Q}{t} \] Substituting this in the equation: \[ P = V \left(\frac{Q}{t}\right) \] \[ P = VI \]
Step 4:Final expression} Thus, the electric power in a circuit is given by: \[ \boxed{P = VI} \] where \(P\) = power (in watts)
\(V\) = potential difference (in volts)
\(I\) = current (in amperes)