Question

Two bulbs are rated: bulb A 100W, 120 V bulb B 10 W, 120 V. If both are connected across a 120V supply, which bulb will consume more energy, When in parallel? Also calculate the current through each bulb in the above cases.

Answer 1

In the case of bulb A, Power: P = `"V"^2/"R"_"A"`

R_A = `"V"^2/"P" = (120 xx 120)/100` = 144 Ω

i.e., Resistance (R_A ) of bulb, A = 144 Ω

Similarly resistance R_B of bulb, B = `"V"^2/"P"`

`= (120 xx 120)/10 = 1440` Ω

When the bulb are connected in Parallel:

Voltage is the same (120 V) across each bulb.

∴ The current in bulb A or I_A = `"V"/"R"_"A" = 120/144 = 0.83` A

∴ The current in bulb B or I_B `= 120/1440` = 0.083 A

Hence, power consumed in bulb A = P_A = `"V"^2/"R"_"A" = (120 xx 120)/144`

= 100 W

and power consumed in bulb B = P_B = `"V"^2/"R"_"B"`

`= (120 xx 120)/1440 = 10 "W"`

Hence, bulb A (100W, 120 V) consumes more energy then bulb B, when both are connected in parallel.