Water is heated with a coil of resistance R connected to domestic supply. The rise of temperature of water will depend on 1. Supply voltage. 2. Current passing through the coil. 3. Time for which voltage is supplied. Select the correct answer from among the following:
- (a)1, 2 and 3
- (b)1 and 2 only
- (c)1 only
- (d)2 and 3 only
Correct — A, 1, 2 and 3. The heat produced by a current is given by Joule's law, H = V·I·t = I²R·t = (V²/R)·t. The temperature rise of the water depends on how much heat the coil delivers, so it depends on the supply voltage, the current through the coil and the time the supply is on — all three. (Because V, I and R are linked by Ohm's law, the three quantities are not independent, but each does affect the heat produced.)
- (b)1 and 2 only — This drops time, yet a longer heating time delivers more energy (H is proportional to t), so time clearly affects the temperature rise.
- (c)1 only — Voltage alone is not enough — the same voltage across a different resistance gives a different current and a different heating rate, and the duration still matters.
- (d)2 and 3 only — This drops voltage, but for a fixed coil the supply voltage sets the current and the power (V²/R), so it does affect the heating.
When current flows through a resistance, electrical energy is converted into heat (the heating effect of current). Joule's law states H = VIt = I²Rt = (V²/R)t. The heat delivered — and hence the temperature rise of the water — grows with voltage, current and the time the supply is switched on.
The question lists three quantities and asks which affect the temperature rise. All appear in Joule's law, so all three matter. Ohm's law (V = IR) links them, which is why voltage, current and resistance are not truly independent choices.
- Joule's law of heating: H = VIt = I²Rt = (V²/R)t.
- Rise in temperature depends on the heat supplied (and on the mass and specific heat of the water).
- Ohm's law V = IR connects voltage, current and resistance.
- Electrical energy consumed equals power multiplied by time, with power P = VI.
All three listed quantities enter Joule's law, so the answer is (a) 1, 2 and 3.
- Forgetting that heating time changes the total energy delivered.
- Treating V, I and R as fully independent — Ohm's law connects them.
Asked as a multi-statement item on what the heat or temperature rise from a current depends on.
No directly related past PYQ was found.
- practice — not a real PYQ
The heat produced in a resistor by a steady current is proportional to
- (a)the current I
- (b)the square of the current, I²
- (c)1/I
- (d)1/I²
Answer(b) the square of the current, I² — from H = I²Rt.
- practice — not a real PYQ
The commercial unit of electrical energy is the
- (a)watt
- (b)joule
- (c)kilowatt-hour
- (d)ampere
Answer(c) kilowatt-hour — energy equals power multiplied by time.