Class 10 > Unit # 15: Current Electricity > Electric Power & Joule's Law

 

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Electric Power, Power Dissipation, and Joule's Law

Q.6 Define Electric Power and Power dissipation. State And explain Joule’s Law.

Electric Power

"The rate at which work is done in an electrical circuit is called electric power. Alternatively, it is defined as the rate of transfer of electrical energy."

Mathematically, electric power ($P$) is given by the product of potential difference ($V$) and current ($I$):

$P = V \cdot I$

Power Dissipation in Resistors

"When an electric current flows through a resistor, electrical energy is converted into heat energy due to collisions between moving charge carriers and the atoms of the conductor. The rate at which heat energy is dissipated into the surrounding air by a resistive component is called power dissipation."

From the definition of power and work ($W = V \cdot Q = V \cdot I \cdot t$), the electrical energy ($W$ or $E$) consumed in a resistor over time $t$ is:

$E = P \cdot t$

$E = (V \cdot I) \cdot t$

Using Ohm's Law ($V = I \cdot R$), we can substitute $V$ to find power dissipation in terms of current and resistance:

$P = (I \cdot R) \cdot I$

$P = I^2 R$

Joule’s Law of Heating

Statement: "When an electric current passes through a conductor, the amount of heat ($H$) produced is directly proportional to the square of the magnitude of the current ($I$), the electrical resistance ($R$) of the conductor, and the time ($t$) for which the current flows."

Mathematical Derivation

According to Joule's Law, heat generated is proportional to:

1. $H \propto I^2$ (Square of current)
2. $H \propto R$ (Resistance of conductor)
3. $H \propto t$ (Time duration)

Combining these factors:

$H \propto I^2 R t$

$H = I^2 R t \quad \text{(in Joules)}$

Where:

• $H$ = Amount of heat produced (measured in Joules, $\text{J}$)
• $I$ = Electric current (measured in Amperes, $\text{A}$)
• $R$ = Electric resistance (measured in Ohms, $\Omega$)
• $t$ = Time interval (measured in seconds, $\text{s}$)

Fig: Conversion of electrical energy into thermal heat energy (Joule heating / Power dissipation) in a resistor.

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