Light bulbs with the power ratings (expressed in watts) given in the figure belo

Question

Light bulbs with the power ratings (expressed in watts) given in the figure below are connected in a circuit. (a ) What current does the voltage source deliver to the circuit? (b) Find the power delivered to each bulb. (Take the bulb resistance to be the same as their normal operating voltage, like 120-v for instance).

Light bulbs with the power ratings (expressed in watts) given in the figure below are connected in a circuit. (a ) What current does the voltage source deliver to the circuit? (b) Find the power delivered to each bulb. (Take the bulb resistance to be the same as their normal operating voltage, like 120 - v for instance).

Explanation / Answer

60 ohm and 100 ohm are connected in parallel, the equivalent resitance is

1/R = 1/ 60 ohm + 1/100 ohm

R = 37.5 ohm

Now 15 ohm , 37.5 ohm and 40 ohm are connected in seris , the net resistance is

R(eq) = 15 ohm +37.5 ohm + 40 ohm = 92.5 ohm

The current in the circuit is

I = V/R(eq) = 120 V/92.5 ohm = 1.29 A

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The power delivered to 15 ohm bulb is

V1 = I R1 = 1.29 A ( 15 W) = 19.35 V

P = V1^2/R = ( 19.35 V)^2/15 ohm = 24.96W

The power delivered to 40 ohm bulb is

V2 = I R2 = 1.29 A ( 40 W) = 51.6 V

P = V^2/R = ( 51.6 V)^2/40 ohm = 66.56W

the current through 60 ohm , 100 ohm branch is

V - V1+ V2 = 120 V - (51.6 V + 19.35 V) = 49.05 V

the current through 60 ohm is

I1 = 49.05 V/ 60 ohm = 0.8175 A

power through 60 ohm bulb is

P( 60ohm) = V^2/R = ( 49.05 V)^2/60 ohm = 40 W

power through 100 ohm bulb is

P( 100ohm) = V^2/R = ( 49.05 V)^2/100 ohm = 24.05 W

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