Question

An electric iron of heating element of resistance $88\Omega$ is used at 220 volts for 2 hours. The electric energy spent, in unit, will be:
A. 0.8
B. 1.1
C. 2.2
D. 8.8

Answer 1

To calculate the energy we need to first calculate the power produced by the electrical system. We will use the formula, $P = VI$ for the same. Then we will substitute this in the formula, $E = Pt$ to calculate the energy spent.

Complete step by step answer:
We know the formula to calculate the electric power produced in a circuit is,
$P = VI$ (Where, p is the electric power; Vis the voltage used; I is the current in amperes)
From ohm’s law, we know that, $I = \dfrac{V}{R}$
On substituting the value if I in the power formula, we get,
$P = \dfrac{{{V^2}}}{R}$
(Now, substitute the value of V and R in the above relation)
$P = \dfrac{{{{220}^2}}}{{88}}$
$\Rightarrow P = 550W$
(Now, for simpler calculations, we will convert watts to kilowatt-hours. This is the commercial unit for calculating the energy consumed by an electrical circuit)
$P = 0.55$kW
So, the formula to calculate the energy consumed is,
$E = Pt$ (where E is the energy consumed; P is the electric power; t is the time)
On substituting the required values in the above formula, we get,
$E = 0.55kW \times 2hrs$
$\Rightarrow E = 1.1$ units
Hence, option (B) is the correct answer.

Note: Kilowatt-hour is the commercial unit of electricity. Therefore, one should calculate the answers in the same unit.
-If the resistances are connected in series, then using $P = {I^2}R$, the power developed will be higher in the resistor of higher value as current will be the same in all resistors.
-If the resistances are connected in parallel, then using $P = \dfrac{{{V^2}}}{R}$, the power developed will be higher in the resistor of a lower value as potential will be the same across all resistors.