A. 0.77 A
Using the relationship:
![P=\frac{V^2}{R}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7BV%5E2%7D%7BR%7D)
where P is the power, V is the voltage, and R the resistance, we can find the resistance of each bulb.
For the first light bulb, P = 60 W and V = 120 V, so the resistance is
![R_1=\frac{V^2}{P}=\frac{(120 V)^2}{60 W}=240 \Omega](https://tex.z-dn.net/?f=R_1%3D%5Cfrac%7BV%5E2%7D%7BP%7D%3D%5Cfrac%7B%28120%20V%29%5E2%7D%7B60%20W%7D%3D240%20%5COmega)
For the second light bulb, P = 200 W and V = 120 V, so the resistance is
![R_1=\frac{V^2}{P}=\frac{(120 V)^2}{200 W}=72 \Omega](https://tex.z-dn.net/?f=R_1%3D%5Cfrac%7BV%5E2%7D%7BP%7D%3D%5Cfrac%7B%28120%20V%29%5E2%7D%7B200%20W%7D%3D72%20%5COmega)
The two light bulbs are connected in series, so their equivalent resistance is
![R=R_1 + R_2 = 240 \Omega + 72 \Omega =312 \Omega](https://tex.z-dn.net/?f=R%3DR_1%20%2B%20R_2%20%3D%20240%20%5COmega%20%2B%2072%20%5COmega%20%3D312%20%5COmega)
The two light bulbs are connected to a voltage of
V = 240 V
So we can find the current through the two bulbs by using Ohm's law:
![I=\frac{V}{R}=\frac{240 V}{312 \Omega}=0.77 A](https://tex.z-dn.net/?f=I%3D%5Cfrac%7BV%7D%7BR%7D%3D%5Cfrac%7B240%20V%7D%7B312%20%5COmega%7D%3D0.77%20A)
B. 142.3 W
The power dissipated in the first bulb is given by:
![P_1=I^2 R_1](https://tex.z-dn.net/?f=P_1%3DI%5E2%20R_1)
where
I = 0.77 A is the current
is the resistance of the bulb
Substituting numbers, we get
![P_1 = (0.77 A)^2 (240 \Omega)=142.3 W](https://tex.z-dn.net/?f=P_1%20%3D%20%280.77%20A%29%5E2%20%28240%20%5COmega%29%3D142.3%20W)
C. 42.7 W
The power dissipated in the second bulb is given by:
![P_2=I^2 R_2](https://tex.z-dn.net/?f=P_2%3DI%5E2%20R_2)
where
I = 0.77 A is the current
is the resistance of the bulb
Substituting numbers, we get
![P_2 = (0.77 A)^2 (72 \Omega)=42.7 W](https://tex.z-dn.net/?f=P_2%20%3D%20%280.77%20A%29%5E2%20%2872%20%5COmega%29%3D42.7%20W)
D. The 60-W bulb burns out very quickly
The power dissipated by the resistance of each light bulb is equal to:
![P=\frac{E}{t}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7BE%7D%7Bt%7D)
where
E is the amount of energy dissipated
t is the time interval
From part B and C we see that the 60 W bulb dissipates more power (142.3 W) than the 200-W bulb (42.7 W). This means that the first bulb dissipates energy faster than the second bulb, so it also burns out faster.