Question

Two electric lamps are rated for \[220\] volts \[60\] watts, and $220$ volts $40$ watts. Find the heat generated in each lamp per second when they are connected in series across $220$ volts.

Answer 1

Hint: Let us get some basic ideas first. Georg Ohm, a German physicist, was the first to identify the relationship between voltage, current, and resistance in a DC electrical circuit. The rate at which energy is absorbed or produced in a circuit is known as electrical power ( P ).

Complete step by step answer:
Power is produced or delivered by a source of energy, such as a voltage, while the associated load absorbs it. For example, light bulbs and heaters collect electrical energy and convert it to heat, light, or both. The higher their wattage figure or rating, the more electricity they are likely to use.

The quantity symbol for power is P, and it is defined as the product of voltage multiplied by current, using the Watt as the unit of measurement ( W ). Prefixes, such as milliwatts or kilowatts, are used to signify the numerous multiples or sub-multiples of a watt. The formula for electrical power may therefore be determined by applying Ohm's rule and substituting for the values of $V, I$, and $R$:
$P = V \times I$
$\Rightarrow P = \dfrac{{{V^2}}}{R}$
$\Rightarrow P = {I^2} \times R$
This formula also helps us to know about the heat generated per second in the lamp.

Given: By using $P = \dfrac{{{V^2}}}{R}$
We can say that:
${R_1} = \dfrac{{{{(220)}^2}}}{{60}} = 806.6\Omega $...........[${R_1}$ is resistance of first lamp]
$\Rightarrow {R_2} = \dfrac{{{{(220)}^2}}}{{40}} = 1210\Omega $..............[${R_2}$ is resistance of second lamp ]
$\Rightarrow I = \dfrac{{220}}{{{R_1} + {R_2}}}$
$\Rightarrow I = \dfrac{{220}}{{806.6 + 1210}} = 0.1$
Now by using formula
${H_1} = {I^2}{R_1}$............[${H_1}$ is heat of first lamp]
$\therefore {H_1} = {(0.1)^2} \times 806.6 = 8.263\,J/s$
$\Rightarrow {H_2} = {I^2}{R_2}$...........[${H_2}$ is heat of second lamp]
$\therefore {H_2} = {(0.1)^2} \times 1210 = 12.43\,J/s$

Hence, the heat generated in both the lamps are 8.263 J/s and 12.43 J/s.

Note: Most light bulbs and lamps produce more heat than light, and knowing when to use a lamp or the sun, depending on the season, can save you a lot of money on energy bills. That means that just two watts out of every 100 watt light bulb are really converted to light. The remainder is being converted to heat.