Question

A current of 3 A flows through a resistor of resistance 4 Ω for 2 minutes. The heat produced is:

• A. 4320 J
• B. 4720 J
• C. 4960 J
• D. 4360 J

Hint:

Formula: \( H = I^2 R t \) gives heat in joules when current is in amperes, resistance in ohms, and time in seconds.

Answer 1

The Correct Option is A

To determine the heat produced when a current flows through a resistor, we use the formula for electrical power dissipation due to resistance, which is given by:

H = I²Rt

where H is the heat produced (in joules), I is the current (in amperes), R is the resistance (in ohms), and t is the time (in seconds).

Given:

• Current, I = 3 A
• Resistance, R = 4 Ω
• Time, t = 2 minutes = 2 × 60 = 120 seconds

Substituting these values into the formula:

H = (3)² × 4 × 120

H = 9 × 4 × 120

H = 36 × 120

H = 4320 J

Therefore, the heat produced is 4320 Joules.

Answer 2

To determine the heat produced by the resistor, we use Joule's Law, which is mathematically represented as:

H = I²RT

Where:

• H is the heat generated in joules (J)
• I is the current in amperes (A)
• R is the resistance in ohms (Ω)
• T is the time in seconds (s)

Given:

• I = 3 A
• R = 4 Ω
• T = 2 minutes = 120 seconds

Substitute the given values into the formula:

H = (3 A)² × 4 Ω × 120 s

Calculating step-by-step:

1. Calculate I²:
   3² = 9
2. Substitute in the equation:
   H = 9 × 4 × 120
3. Multiply these values:
   H = 4320 J

Thus, the heat produced is 4320 J.