Question

Find the amount of power generated in each bulb if we connect a 40 W bulb in series with a 120 W bulb to 120 volts AC circuit.

Answer 1

Given - Resistance and voltage

Find - Power generated

Solution - The amount of power generated is 90 Watt.

Power, voltage and resistance are related to each other by the formula -

P = V²/R. Here, p is power, V is voltage and R is resistance.

The two bulbs are connected in series, so the combined resistance will be -

R = R1 + R2

R = 40 + 120

R = 160 ohm

Now calculating the value of Power generated by keeping the values in formula-

$p \: = \frac{ {120}^{2} }{160}$

p = 90 Watt

Thus, the amount of power generated is 90 Watt.

Answer 2

The amount of power generated in 40W bulb is 22.5W   and 120W bulb is 7.5W if  a 40 W bulb connected in series with a 120 W bulb to 120 volts AC circuit.

Assuming Bulbs 40W and 120W are rated for 120V

P = V²/R  

R =  V²/P

R₄₀ = 120²/40  = 360 Ω

R₁₂₀ = 120²/120 = 120 Ω

Resistance in Series  R  = 360 + 120 Ω

= 480 Ω

I =V/R   Current in circuit

I = 120/480

I = 1/4 A

P = I²R

P₄₀ = I²R₄₀

= (1/4)² 360

= 22.5 W

P₁₂₀ = I²R₄₀

= (1/4)² 120

=7.5 W

The amount of power generated in 40W bulb is 22.5W   and 120W bulb is 7.5W