In a circuit, three bulbs are connected in series and in another circuit, three bulbs are connected in parallel. The magnitude of the emf source for both circuits is the same. How can you explain the difference in brightness of bulbs in both circuits?

or alternatively, in terms of current I:

P=I2R

where:

• $P$ is the power dissipated (which determines brightness),
• $V$ is the voltage across the bulb,
• $R$ is the resistance of the bulb,
• $I$ is the current through the bulb.

Series Circuit:

In a series circuit, the same current flows through all the bulbs, but the voltage across each bulb will be divided according to its resistance. The total resistance in the series circuit is the sum of the individual resistances of the bulbs:

Rtotal=R1+R2+R3​

Since the current is the same through all bulbs, the voltage drop across each bulb is proportional to its resistance (by Ohm’s Law):

V_i=IR_i    for each bulb

• In a series circuit, because the current is the same for all bulbs, the brightness of each bulb depends on its resistance. If the bulbs are identical, each will have the same voltage drop and therefore the same brightness.

Parallel Circuit:

In a parallel circuit, each bulb gets the same voltage (the full source voltage), but the current through each bulb depends on its resistance. The total resistance of the parallel circuit is given by:

1/Rtotal=1/R1+1/R2+1/R3​

Each bulb experiences the same voltage, so the power dissipated by each bulb is determined by the current through it. Since lower resistance bulbs draw more current, they dissipate more power and are brighter.

Comparison of Brightness:

• In the series circuit: The current is lower (because the total resistance is higher), so the power (brightness) of each bulb will be less than in the parallel circuit.
• In the parallel circuit: Since each bulb gets the full voltage, and the total resistance is lower (compared to the series case), the current is higher, which means the bulbs will dissipate more power and thus be brighter than in the series circuit.

Conclusion:

• Series circuit: The bulbs are dimmer because the current is lower, and the power dissipation is less.
• Parallel circuit: The bulbs are brighter because each bulb gets the full voltage and the current is higher, leading to more power dissipation.