A 100W 220 V bulb is connected to a supply of 110 V calculate the power dissipated by this bulb

The most confusing question we received that if two bulbs are connected in series and then in parallel, which one will glow brighter and what are the exact reasons? Well, there are lots of info around the web, but we will go in a very step by step details to calculate the exact values to clear the confusion.

First of all, keep in mind that the bulb having a high resistance and dissipate more power in the circuit (no matter series or parallel) will glow brighter. In other words, the brightness of the bulb depends on voltage, current (V x I = Power) as well as resistance.

Also, keep in mind that power dissipated in Watts is not the unit of brightness. Unit of brightness is lumens (denoted by lm which is SI derived unit of luminous flux) also known as candela (base unit of luminous intensity). But the light brightness is directly proportional to the bulb wattage. That’s why the more wattage a bulb is using will glow brighter.

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When Bulbs are Connected in Series

Ratings of bulbs Wattage are different and connected in a series circuit:

Suppose we have two bulbs each of 80W (Bulb 1) and 100W (Bulb 2), rated voltages of both bulbs are 220V and connected in series with a supply voltage of 220V AC. In that case, the bulb with high resistance and more power dissipation will glow brighter than the other one. i.e. 80W Bulb (1) will glow brighter and bulb (2) of 100W will dimmer in series connection. In short, In series, both bulbs have the same current flowing through them. The bulb with the higher resistance will have a greater voltage drop across it and therefore have a higher power dissipation and brightness. How? Let see the below calculations and examples.

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Power

P = V x I or P = I2 R or P = V2/R

Now, the resistance of Bulb 1 (80W);

We know that current is same and voltage are additive in a series circuit but the rated voltage of bulbs are 220V. i.e.

Voltage in series circuit: VT = V1 + V2 + V3 …+ Vn

Current in series circuit: IT = I1 = I2 = I3 …In

Therefore,

R = V2 / P80

R80W = 2202 / 80W

R80W = 605Ω

And, the resistance of Bulb 2 (100W);

R = V2 / P100

R100W = 2202 / 100W

R100W = 484Ω

Now, Current;

I = V/R

= V / (R80W + R100W)

= 220V / (605Ω + 484Ω)

I = 0.202A

Now,

Power dissipated by Bulb 1 (80W)

P = I2R

P80W = (0.202A)2 x 605Ω

P80W = 24.68 W

Power dissipated by Bulb 2 (100W)

P = I2R100

P100W = (0.202A)2 x 484Ω

P100W = 19.74 W

Hence, proved power dissipated P80W > P100W i.e. Bulb 1 (80W) is greater in power dissipation than bulb 2 (100W). Therefore, the 80W bulb is brighter than 100W bulb when connected in series.

You may also find the voltage drop across each bulb and then find the power dissipation by P = V x I as follows to verify the case.

V = I x R or I = V/R or R = V/I … (Basic Ohm’s Law)

For Bulb 1 (80W)

V80 = I x R80 = 0.202 x 605Ω = 122.3V

V80 = 122.3V

For Bulb 2 (100W)

V100 = I x R100 = 0.202 x 484Ω = 97.7V

V100 = 97.7V

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Now,

Power dissipated by Bulb 1 (80W)

P = V280/R80

P80W = 122.32V / 605Ω

P80W = 24.7 W

Power dissipated by Bulb 2 (100W)

P = V2100/R100

P100W = 97.722V / 484Ω

P100W = 19.74 W

Total Voltage in the series circuit

VT = V80 + V100 = 122.3 + 97.7 = 220V

Again proved that 80W bulb is greater in power dissipation than 100W bulb when connected in series. Hence, 80W bulb will glow brighter than 100W bulb when connected in series.

When Bulbs are Connected in Parallel

Ratings of bulbs Wattage are different and connected in the parallel circuit:

Now we have the same two bulbs each of 80W (Bulb 1) and 100W (Bulb 2) connected in parallel across the supply voltage of 220V AC. In that case, the same will happen i.e. the bulb with more current and high power dissipation will glow brighter than the other one. This time, 100W Bulb (2) will glow brighter and bulb 1 of 80W will dimmer. In short, In parallel, both bulbs have the same voltage across them. The bulb with the lower resistance will conduct more current and therefore have a higher power dissipation and brightness. Confused? as the case has been reversed. Let see the below calculations and examples to clear the confusion.

Power

P = V x I or P = I2 R or P = V2/R

Now, the resistance of Bulb 1 (80W);

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We know that voltages are the same in the parallel circuit and the rated voltage of bulbs are 220V. i.e.

Voltage in Parallel Circuit: VT = V1 = V2 = V3 …Vn

Current in parallel circuit: IT = I1 + I2 + I3 …In

Therefore,

R = V2 / P

R80W = 2202 / 80W

R80W = 605Ω

And, the resistance of Bulb 2 (100W);

R = V2 / P

R100W = 2202 / 100W

R100W = 484Ω

Now,

Power dissipated by Bulb 1 (80W) as voltages are same in a parallel circuit.

P = V2/R1

P80W = (220V)2 / 605Ω

P80W = 80 W

Power dissipated by Bulb 2 (100W)

P = V2/R2

P100W = (220V)2 / 484Ω

P100W = 100 W

Hence, proved P100W > P80W i.e. Bulb 2 (100W) is greater in power dissipation than bulb 1 (80W). Therefore, the 100W bulb is brighter than 80W bulb when connected in parallel.

To verify the above case, You may also find the current for each bulb and then find the power dissipation by P = V x I as follows. We used the rated voltage of the bulb which is 220V.

I = P / V

For Bulb 1 (80W)

I80 = P80 / 220 = 80W / 220 = 0.364A

I80 = 0.364A

For Bulb 2 (100W)

I100 = P100 / 220 = 100W / 220 = 0.455A

I100 = 0.455A

Now,

Power dissipated by Bulb 1 (80W) as voltages are same in the parallel circuit.

P = I2R1

P80W = 0.3642A x 605Ω

P80W = 80 W

Power dissipated by Bulb 2 (100W)

P = I2R2

P100W = 0.4552A x 484Ω

P100W = 100 W

Total Current in the parallel circuit

IT = I1 + I2 = 0.364 + 0.455 = 0.818A

Again proved that 100W bulb is greater in power dissipation than the 80W bulb when connected in parallel. Hence, 100W bulb will glow brighter than 80W bulb when connected in parallel.

Without Calculations & Examples

Calculations and examples are for newbies. To make it simple, keep the fact in mind that always, The bulb with a “high power” will have “less resistance”. The filament of the bulb with a high rating is thicker than the lower wattage. In our case, the filament of the 80W bulb is thinner than the 100W bulb.

In other words, 100 Watt bulb has less resistance and 80 Watt bulb has a high resistance.

When bulbs connected in Series

We know that current in a series circuit is same at each point mean both bulbs getting the same current and voltages are different. Obliviously, the voltage drop across higher resistance bulb (80W) will be more. So the 80W bulb will glow brighter as compared to 100W bulb connected in series because the same current is flowing through both of the bulbs where the 80W bulb has more resistance due to lower wattage as the filament is thinner means it dissipates more power (P=V2/R where power is directly proportional to the voltage and inversely proportional to the resistance) and produce higher heat & light than the 100 W bulb.

When Bulbs are connected in Parallel

We also know that voltage in a parallel circuit is the same at each section which means both of the bulbs have the same voltage drop. Now more current will flow in the bulb which has less resistance which is 100W bulb this time which means 100W bulb dissipate more power than 80W bulb (P=I2R) where current and resistance are directly proportional to the power. Hence, 100W bulb will glow brighter in a parallel circuit.

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How to know if Bulbs are Connected in series or Parallel?

Most of the household electrical wiring & installation are wired in parallel or series-parallel instead of series as parallel wiring has some advantages over a series wiring. So we may notice that higher rated bulb glows more brightly as compared to lower wattage rated bulbs. In that case, 100W bulb glows more brightly than 60W or 80W bulb.

Now, You should know that the light bulb with higher power rating will glow brighter when connected in parallel and the light bulb with less power rating will glow brighter in case of series wiring and Vice versa.

Key Points:

• In a series circuit, 80W bulb glows brighter due to high power dissipation instead of a 100W bulb.
• In a parallel circuit, 100W bulb glows brighter due to high power dissipation instead of an 80W bulb.
• The bulb which dissipates more power will glow brighter.
• In series, both bulbs have the same current flowing through them. The bulb with the higher resistance will have a greater voltage drop across it and therefore have a higher power dissipation and brightness.
• In parallel, both bulbs have the same voltage across them. The bulb with the lower resistance will conduct more current and therefore have a higher power dissipation and brightness.
• Most household electrical wiring bulbs are wired in parallel.

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