Question

A $230 V$, $115 V$ filament lamp works in a circuit for $10$ minutes,
(a) What is the current flowing through the bulb?
(b) How much is the quantity of charge that flows through the bulb in $10$ minutes?

Answer 1

In the given question, we have given power and voltage of the bulb. Power is defined as the product of current and voltage. We know the value of current. Charge is equal to the product of current and time. As we have calculated current in the previous calculations, we will use it to find the charge flowing.

Complete step-by-step solution:
Given: Voltage $=230 V$
Power, $P=115W$
Time taken, $t=10$ minutes
a) As we know, $Power = Voltage \times current$
$P =VI$
We need to find out the current flowing.
$I = \dfrac{P}{V}$
Put the given values in the above formula:
$I = \dfrac{115}{230}$
$I = 0.5A$
The current flowing through the bulb is $0.5A$
b) We need to calculate the charge that flows through the bulb in a given time.
Current is related with charge and time taken by the given formula:
$I = \dfrac{Q}{t}$
$\implies Q = I \times t$
$t = 10$ minutes $= 600$ seconds
$Q = 0.5 \times 600 = 300C$
Charge that flows through the bulb in $10$ minutes is $300C$.

Note: Electrical power can also be described as the rate by which current is carried. If one joule of work is either received or transported at a fixed rate of one second, the corresponding power will equal one watt. Then we can assume that one watt is equivalent to one joule per second, and electrical power can be expressed as the rate of performing work or transferring energy.