Question

A 2.5 kW immersion heater is used to heat water. Calculate:
1. The operating voltage of the heater if its resistance is 24Ω
2. The electrical energy converted to heat energy in 2 hours.

Answer 1

Given:

A 2.5 kW immersion heater is used to heat water.

To Find:

1)The operating voltage of the heater if its resistance is 24 ohms

2)The electrical energy converted to heat energy in 2 hours.

Solution:

Power rating of immersion heater = 2.5 kW

Power of a electric appliance is defined as the product of current and voltage.

             P = VI

V in volts     I in amperes

P in watts.

V = IR  (ohms law)

$I = \frac{V}{R}$

R = 24 ohms

V = operating voltage

P = VI

$V = \frac{P}{R}\\ V = \frac{2500}{24} \\V = 104.16 volts.$

Heat energy

  $H = I^{2} RT$

$I = \frac{V}{R} \\\\I = \frac{104.16}{24} \\I = 4.34 amps.\\H = I^{2} RT\\H = 4.34^{2}(24)(2)(3600)\\ H = 3254791.68 joules$

The operating voltage of heater = 104.16 volts

The electrical energy converted to heat energy in 2 hours is 3254791.68 joules.