Question

An electric heater of resistance $115\Omega $ is made to work on $230V$ supply.
(A) What will be the current through this heater while it is working?
(B) Calculate the power of this heater.
(C) Calculate the heat generated by the heater if it works for 10 minutes.

Answer 1

Hint
Electric heater converts electrical energy into heat energy. To solve this question we use the formulas of Resistance, power and heat. The formula for heat is derived from the formula for power, by simply multiplying with time.
$\Rightarrow I = \dfrac{V}{R}$; (in amperes)
$\Rightarrow P = {I^2}RT$ (in Watt)
$\Rightarrow H = P \times t$(in Joules)

Complete step by step answer
Part a) To determine the current flow through the heater while it is working, we can use the ohm’s law, which is-
$\Rightarrow V = IR$
Here, V is the potential difference, I is the current flow, and R is the resistance in the circuit.
Therefore If $V = 230V$and $R = 115\Omega $, I is given by-
$\Rightarrow I = \dfrac{V}{R}$
$\Rightarrow I = \dfrac{{230}}{{115}}$
$\Rightarrow I = 2A$
The unit of current is Ampere(A).
Part b) Now that we know the value of I the value of power can be calculated by-
$\Rightarrow P = {I^2}R$
$\Rightarrow P = 4 \times 115$
$\Rightarrow P = 460W$
The unit of power is Watt(W) ; it is defined as $J/s$ (Joules per second).
Alternatively, power can also be calculated using the value of V as-
$\Rightarrow P = \dfrac{{{V^2}}}{R}$
Part c) Power is defined as heat (or energy) produced per unit time. So we can multiply power with the total time of operation to get the value of heat produced by the heater.
For this, the first step is to convert time into seconds.
$\Rightarrow t = 10 \times 60 = 600\sec $
Now, $H = P \times t$
$\Rightarrow H = 460 \times 600$
$\Rightarrow H = 276000J$
Unit of heat is Joules(J) ; it is defined as $Nm$(Newton meter).

Note
Heaters are designed to have a high value of resistance, this resistance is what produces the heating effect. Almost all of the heating devices use Nichrome, which is an alloy of $80\% $ Nickel and $20\% $chromium as their heating element. The outer layer of Nichrome is oxidised which prevents any further corrosion to the inner material at high temperatures. It also has a very high resistivity which makes it an optimum material to use in heating devices.