If a 10-watt lamp and a 100-watt lamp, each rated at 120 volts, are connected in series to a 240-volt source, what will the voltage across the 10-watt lamp be?

In a series circuit, the total voltage is divided among the components based on their resistance. The resistance of each lamp can be calculated using the formula ( R = \frac{V^2}{P} ), where ( V ) is the voltage rating and ( P ) is the power.

For the 10-watt lamp:

• ( R_{10} = \frac{120^2}{10} = 1440 , \Omega )

For the 100-watt lamp:

• ( R_{100} = \frac{120^2}{100} = 144 , \Omega )

The total resistance in the circuit is the sum of the resistances:

• ( R_{total} = R_{10} + R_{100} = 1440 + 144 = 1584 , \Omega )

Next, we can find the total current flowing through the series circuit using Ohm's law ( I = \frac{V}{R} ):

• ( I = \frac{240}{1584} \approx 0.151 , A )

To find the voltage across the 10-watt lamp, we can apply Ohm's Law again, using