Arrange the following cases in ascending order of heat generated in the resistances during \( 5 \) s of flow of current.
A. \( I = 5 \) A, \( R = 20\,\Omega \)
B. \( V = 50 \) Volt, \( R = 4\,\Omega \)
C. \( I = 4 \) A, \( R = 30\,\Omega \)
D. \( V = 60 \) Volt, \( R = 10\,\Omega \)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → D, C, A, B
The heat produced in a resistor (Joule heating) is \( H = I^{2}Rt \), or \( H = V^{2}t/R \) when the voltage is given; here \( t = 5\,\mathrm{s} \) for every case.
A. \( I = 5 \) A, \( R = 20\,\Omega \) — \( H = (5)^{2}(20)(5) = 2500\,\mathrm{J} \)
B. \( V = 50 \) Volt, \( R = 4\,\Omega \) — \( H = (50)^{2}(5)/4 = 3125\,\mathrm{J} \)
C. \( I = 4 \) A, \( R = 30\,\Omega \) — \( H = (4)^{2}(30)(5) = 2400\,\mathrm{J} \)
D. \( V = 60 \) Volt, \( R = 10\,\Omega \) — \( H = (60)^{2}(5)/10 = 1800\,\mathrm{J} \)
Ascending order: D (1800 J), C (2400 J), A (2500 J), B (3125 J), that is D, C, A, B.