In heating effect, if ‘I’ is the current flowing through the conductor in ‘t’ seconds having a resistance ‘R’,

Question

In heating effect, if ‘I’ is the current flowing through the conductor in ‘t’ seconds having a resistance ‘R’, then the electrical energy supplied is _______.

Examoogle · Accepted Answer

The correct answer is Option A: I^{2}Rt 	ext{ joules}. According to Joule's law of heating, the electrical energy $H$ dissipated as heat in a resistor $R$ when a current $I$ flows for time $t$ is directly proportional to the square of the current, the resistance, and the time duration. The mathematical expression is $H = I^{2}Rt$ joules.

Step-by-Step Solution & Concepts:
According to Joule's law of heating, the electrical energy $H$ dissipated as heat in a resistor $R$ when a current $I$ flows for time $t$ is directly proportional to the square of the current, the resistance, and the time duration. The mathematical expression is $H = I^{2}Rt$ joules.

Working Principle: As electric charge moves through a conductor, it undergoes collisions with the atoms of the lattice structure. These collisions convert the kinetic energy gained from the electric field into vibrational energy (heat) of the atoms. The power dissipated is defined by $P = VI$, and substituting $V = IR$ from Ohm's Law leads to $P = I^{2}R$. Multiplying power by time gives the total energy.

Key Formulas: $H = I^{2}Rt$ — Joule's law of heating; $P = I^{2}R$ — Electric power dissipation in a resistor; $W = VIt$ — Work done by moving charge $Q$ where $Q = It$

Key Points: Joule's law holds for purely resistive circuits where all electrical energy is converted to thermal energy.; The energy dissipated is proportional to the square of the current, making it sensitive to load variations.; SI unit of electrical energy is Joule ($J$), where $1	ext{ J} = 1	ext{ W} \cdot 	ext{ s}$.

Advantages: Basis for operation of heating appliances like electric iron, heater, and fuses.; Allows for controlled thermal output in industrial processes.

Disadvantages: Unwanted energy loss in transmission lines and electrical machines causing overheating.; Reduces the efficiency of electrical systems due to $I^{2}R$ losses.

Applications: Electric toasters and water heaters; Incandescent bulbs; Electric fuses for circuit protection

Additional Info: Option B ($IR^{2}/t$) is dimensionally incorrect.. Option C ($I^{2}R/t$) implies power divided by time, which is not energy.. Option D ($IR^{2}t$) is incorrect as the exponent belongs to the current $I$.

Answer: A is correct — The electrical energy dissipated in a resistive circuit is given by the product of the square of the current, resistance, and time ($I^{2}Rt$).

Exam Tip: Always remember that $I^{2}R$ losses are termed as copper losses in transformers and DC machines; they are the most significant source of heat in electrical machinery.

Examoogle · Answer

Option B: IR^{2}/t 	ext{ joules}

Examoogle · Answer

Option C: I^{2}R/t 	ext{ joules}

Examoogle · Answer

Option D: IR^{2}t 	ext{ joules}

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