# Question #e8cce

Feb 27, 2016

Lamp marked with lower wattage will glow brighter.

#### Explanation:

Explanation:

The brightness in an electric lamp is produced due to heating of element (Resistance) which is the directly related to power dissipated in it. More bright means more power dissipated. Power is measured in Watts (joules per second)

Let $V$ be voltage applied, $I$ current flowing, $R$ be the resistance and $P$ power consumed in a lamp, then

$\text{Watt"="Volt" xx "Ampere}$
or $P = V I$.......(1)

Since source voltage is same for both the lamps it follows that the lamp with higher wattage will draw higher current. It is possible only if the lower lamp wattage has higher resistance as compared to the lamp with higher wattage.

As we know that

Voltage = current $\times$ resistance
or $V = I R$.........(2)

Combining relationships (1) and (2) we obtain
$P = {I}^{2} R = {V}^{2} / R$..........(3)

In the given problem both lamps are connected in series and a constant current is applied to both the lamps.

Using first part of the expression (3) above
$P = {I}^{2} R$
we see that for the same current more power will be dissipated in the lamp which has higher resistance. That is the lamp with lower wattage.