Question

A heater joined in series with a 3W bulb is connected to the mains. If the 3W bulb is replaced by an 11W bulb, the heat produced by the heater,
A.)Increases
B.)Decreases
C.)Remains the same
D.)None of the above

Answer 1

Hint: If we increase the power rating of the bulb, we are increasing the resistance of the bulb, the bulb with higher power rating will have more resistance. Since the heater is connected in series with this bulb, the resistance of the whole circuit increases and as a result, the current through the heater decreases.

Complete step by step answer:
Considering we have two bulbs of 3W and 11W, we connect the bulb of 3W into a circuit containing a heater. Let i be the current flowing across the bulb, then the power dissipation of the bulb can be written as,

$3W={{i}^{2}}{{R}_{1}}$ … Equation (1)
Where ${{R}_{1}}$ is the resistance offered by the 3W bulb.

Next, we will connect the 11W bulb in the place of the 3W bulb, suppose the current across the bulb is i, then the power of the bulb can be written as,

$11W={{i}^{2}}{{R}_{2}}$ …. equation (2)
Where ${{R}_{2}}$ is the resistance offered by the 11 W bulb.

From equation (1) and (2) we can understand that ${{R}_{2}}>{{R}_{1}}$, which means the 11W bulb offers more resistance compared to the 3W bulb.

So, since the 11 W bulb is connected in series with the heater, the resistance of the whole circuit increases, so, the amount of current flowing through the circuit decreases.

According to Joule’s law of heating, the heat produced in a circuit is given by, $H={{i}^{2}}Rt$, from the equation, it is clear that the heat produced is directly proportional to the current across the circuit. So, as the current decreases, the amount of heat produced decreases.
So, the answer to the question is option (B).

Note:
Electrical Power, ( P ) in a circuit is defined as the rate at which energy is being absorbed or produced in a circuit. A source of energy such as a battery will produce or provide power while the connected load absorbs it. Light bulbs and heaters, for example, are electrical appliances that absorb electrical power and convert it into either heat, or light, or both. The higher their value or rating in watts, the more electrical power they are likely to consume.
$P=\dfrac{{{V}^{2}}}{R}$

When current flows through a conductor, usually heat is generated in a conductor. The heating effect produced by an electric current depends mainly on three factors:

The resistance, ‘R’ of the conductor. Higher the resistance higher will be the heat produced.
The time,’ t’ for which current flows through the conductor. The longer the time the current flows through the conductor, the larger will be the amount of heat produced.

Let ‘I’ be the amount of current flowing through the circuit or appliance. The higher the current, the larger will be the amount of heat generated in the conductor.

The heating effect produced by an electric current, ‘I’ through a conductor of resistance, R for a time, t is given by $H={{I}^{2}}Rt$. This equation is known as Joule’s equation of electrical heating.