Power Dissipated By Each Of Two Bulbs Connected In Series
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Power Dissipated By Each Of Two Bulbs Connected In Series

An incandescent light bulb rated at 60 W will dissipate 60 W of heat and light when connected across a 100 V ideal voltage source. A 100 W bulb will dissipate 100 W when connected across the same source. If the bulbs are connected in series across the same source, determine the power that either one of the two bulbs will dissipate.

The strings: S7P3A32 (force - push).

The math:
Pj Problem of Interest is of type force (push).

Equations of interest: V = IR; P = IV; P = I2R

Figure 1.1 is bulb 1 connected to the voltage source.
So, current, I = P/V = 60/100 = 0.6 A.
So, R1 = P/I2 = 60/0.36 = 166.7 Ω

Figure 1.2 is bulb 2 connected to the voltage source.
So, current, I = P/V = 100/100 = 1 A
So, R2 = P/I2 = 100/1 = 100 Ω

Figure 1.3 is both bulbs connected in series to the voltage source.
So, Total circuit resistance, RT = 166.7 + 100 = 266.7 Ω
So, current, I = 100/266.7 = 0.375 A
VR1 = (166.7/266.7)100 = 62.51 V
So, Power dissipated by bulb one = 0.375 x 62.51 = 23.44 W.
VR2 = (100/266.7)100 = 37.5 V
So, Power dissipated by bulb two = 37.5 x 0.375 = 14.06 W.

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