Power Drawn by Bulbs in Series

The question asks for the total power drawn when three identical bulbs, each rated 60 watts at 200 volts, are connected in series to a 200-volt supply.

First, we need to determine the resistance of a single bulb using its given rating. The power ($P$) dissipated by a resistor with resistance ($R$) across which a voltage ($V$) is applied is given by the formula:

\(P = \frac{V^2}{R}\)

From this, we can find the resistance of one bulb:

\(R = \frac{V^2}{P}\)

Given rating for one bulb:

• Rated Voltage (\(V_{rated}\)) = 200 volts
• Rated Power (\(P_{rated}\)) = 60 watts

Resistance of one bulb (\(R\)):

\(R = \frac{(200 \text{ V})^2}{60 \text{ W}} = \frac{40000}{60} \Omega = \frac{4000}{6} \Omega = \frac{2000}{3} \Omega\)

Now, three such identical bulbs are connected in series. In a series connection, the total resistance (\(R_{total}\)) is the sum of the individual resistances:

\(R_{total} = R_1 + R_2 + R_3\)

Since the bulbs are identical (\(R_1 = R_2 = R_3 = R\)):

\(R_{total} = R + R + R = 3R\)

Substitute the value of \(R\):

\(R_{total} = 3 \times \frac{2000}{3} \Omega = 2000 \Omega\)

These three bulbs in series are connected to a 200-volt supply. The total voltage supplied (\(V_{supply}\)) is 200 volts.

The total current (\(I\)) flowing through the series circuit can be found using Ohm's Law:

\(I = \frac{V_{supply}}{R_{total}}\)

\(I = \frac{200 \text{ V}}{2000 \Omega} = \frac{1}{10} \text{ A} = 0.1 \text{ A}\)

Finally, the total power drawn by the circuit (\(P_{drawn}\)) from the supply is given by:

\(P_{drawn} = V_{supply} \times I\)

Substitute the values of \(V_{supply}\) and \(I\):

\(P_{drawn} = 200 \text{ V} \times 0.1 \text{ A} = 20 \text{ W}\)

Alternatively, we can calculate the total power using the total current and total resistance:

\(P_{drawn} = I^2 \times R_{total}\)

\(P_{drawn} = (0.1 \text{ A})^2 \times 2000 \Omega = (0.01 \text{ A}^2) \times 2000 \Omega = 20 \text{ W}\)

Both methods yield the same result.

Thus, the total power drawn by the three identical bulbs connected in series to a 200-volt supply is 20 watts.