Question

A torch bulb is rated at 3V and 600mA. Calculate its a) Power b) Resistance c) Energy consumed if it is lighted for 4 Hrs.

Answer 1

Hint: In this solution, the power of the bulb, and its energy will both be dependent on the voltage and the current in the circuit. The energy will also depend on the time for which the bulb remains on.

Formula used: In this solution, we will use the following formula:
- Power dissipated in the bulb: $P = Vi$ where $V$ is the voltage and $i$ is the current in the bulb
- Resistance of the bulb: $R = \dfrac{V}{i}$
- Energy consumed by the bulb: $E = P.t$

Complete step by step answer:
We’ve been given that a torch bulb is rated at 3V and 600mA. Then let us start by calculating the power in the bulb as
$P = Vi$
Substituting the value of $V = 3V$ and $i = 600mA = 0.6A$, we get
$P = 3 \times 0.6$
Which gives us the power as
$P = 1.8\,{\text{W}}$
For part(b), we can calculate the resistance of the bulb as
$R = \dfrac{V}{i}$
Substituting the value of $V = 3V$ and $i = 0.6\,{\text{A}}$, we get
$R = \dfrac{3}{{0.6}}$
Which gives us the resistance of the bulb as
$R = 1.8\,\Omega $
For part (c), the energy consumed by the bulb will be a product of the power of the bulb and the time for which it remains on which can be calculated as
$E = Pt$
Substituting the value of $P = 1.8\,{\text{W}}$ and $t = 4 \times 3600\sec $, we get
$E = 1.8 \times 4 \times 3600$
$ \Rightarrow E = 25920\,J$

Note: We should be confused between the power and the energy of the bulb as the power of the bulb is the energy utilized by the bulb per unit of time. While calculating the power, we should be careful that the units of time are in the SI unit system which is seconds as this will give us the energy utilization in Joules.