Question

A torch bulb is rated at 5V and 500mA. Calculate its
(i) Power
(ii) Resistance
(iii) Energy consumed when it is lighted for \[4hours\] .

Answer 1

Hint: The question clearly tells us to calculate the three quantities, We know that, Power of the torch bulb will be calculated by multiplying the rated current and voltage. Resistance is often calculated by dividing voltage by current. The energy absorbed by the torch bulb will be calculated by multiplying power and the time given.

Complete step by step solution:
In the question it is given that the torch bulb is rated at:
Current of \[500mA\] and
Voltage of \[5V\]
Since we know that the SI unit of current is Amperes, and thus we convert mili-Amperes to Amperes by multiplying it with \[{10^{ - 3}}\] .
\[I = 500 \times {10^{ - 3}}\]
\[V = 5V\]
Where,
\[I\] is rated current of the torch bulb
\[V\] is rated voltage of the torch bulb
Power is defined as the amount of energy converted per unit of time. It is a scalar quantity.
Si unit of power is \[Watts(W)\] .
Thus,
(i) \[Power = current \times voltage\]
\[ \Rightarrow P = I \times V\]
Putting the values as given:
\[P = 500 \times {10^{ - 3}} \times 5\]
Therefore, we obtain:
\[P = 2.5W\]
Therefore, this is the required power of the torch bulb.

(ii) Now we need to calculate the Resistance of the torch bulb.
From ohm's law, we know that the resistance can be obtained by calculating the ratio of voltage and current.
\[R = \dfrac{V}{I}\]
Where,
\[R\] is the resistance of the torch bulb.
Resistance is defined as the parameter that opposes the current flow in the device.
Putting the values, we obtain:
\[R = \dfrac{5}{{500 \times {{10}^{ - 3}}}}\]
Thus, we obtain:
\[R = 10\Omega \]
Therefore, this is the obtained resistance of the torch bulb.

(iii) Energy consumed when it is lighted for \[4hours\] implies the amount of power or energy consumed in \[4hours\] .
Energy consumed can be calculated by multiplying power with the time given.
\[E = P \times t\]
Where,
\[E\] is the energy consumed.
\[t\] is \[4hours\]
Putting the values we obtain:
\[E = 2.5 \times 4\]
Thus, we obtain
\[E = 10J\] .

Note: Ohm’s law states that the current flowing through the conductor is directly proportional to the voltage applied across the two points given quantities like pressure and temperature remain constant. This the constant of proportionality is \[R\] , and it is defined as the resistance of the conductor. Unit of energy consumed can also be \[kW-hr\] .