Question

Out of 60W and 40W lamps, which one has a higher electrical resistance when in use.

Answer 1

Hint:The power is defined as the rate of energy transferred and it is expressed in terms of watts (W). Resistance is defined as the hurdles or obstacles in the motion current flow. There is a direct relation between the power and resistance of a device.

Formula used:The formula of the power of the device is given by,
$\Rightarrow P={\displaystyle \frac{V^2}{R}}$
Where power is P. the potential difference is V and the resistance is R.

Complete step by step solution:
It is asked in the problem that out of 60W and 40W lamps, which one has a higher electrical resistance. Let us consider that both the lamps are used in the circuit having the same power source but one by one.

The formula of the power of the device is given by,

$\Rightarrow P={\displaystyle \frac{V^2}{R}}$
Where power is P, the potential difference is V and the resistance is R.

Here we can observe that the power is inversely proportional to the resistance of the circuit.

$\Rightarrow P\propto {\displaystyle \frac{1}{R}}$

Where power is P and resistance is R.
Here we can see that if the power is more than the resistance will be less.
Here we can see that if the power is more than the resistance will be less and if the power is less than the resistance is more. So out of both the lamps the lamp having less power is 40 W and therefore it will have more resistance when used.

The lamp which will have higher resistance in use is the lamp with power 40 W.

Note:The resistance of a device should be small otherwise the losses in the circuit will be very large and then the power drainage will be also high. The Ohm’s law gives us the relation between the potential difference, the current and the resistance of the circuit.