Answer to Question #124910 in Classical Mechanics for Stefanie Hernandez-Mendez

Question

Consider three electric bulbs. Voltage drop across bulb #1 is V and current passing through it is I. Voltage drop across bulb #2 is 2V with current passing through it I/4. Voltage drop across bulb #3 is V/8 and current passing through it is 4I.

Which bulb produces the greatest illumination?

It is impossible to answer without resistances of bulbs given. or
Bulb #3 because it has greatest current. or
Bulb #2 because it has greatest voltage drop. or
Bulb #1 because of the greatest power dissipated.

Answer 1

The illumination corresponds to power that the bulb consumes. The power is current times voltage, ot

$$P=IV.$$

Therefore, for the three bulbs we have

$$P_1=I_1V_1=IV,\\\space\\ P_2=I_2V_2=\frac{I}{4}\cdot{2V}=\frac{IV}{2},\\\space\\ P_3=I_3V_3=4I\cdot\frac{V}{8}=\frac{IV}{2}.$$

Therefore, the first bulb is the brightest.