A 25 W and a 100 W bulb are joined in series and connected to the mains. Which bulb will glow bright

Q: Why doesn't the 100W bulb glow brighter? It has a higher wattage!

The 100W rating is only valid when the bulb is connected to its rated voltage (like directly to the mains in parallel). In a series circuit, it doesn't get its full rated voltage, so it doesn't consume 100W.

Q: What does the wattage rating on a bulb actually mean?

It indicates the power the bulb will consume if it is operated at its specified rated voltage. It is a way to tell you the bulb's internal resistance.

Q: Would the answer change if the bulbs were connected in parallel?

Yes! In parallel, both bulbs get the same voltage. Using the formula $P = \frac{V^2}{R}$, the bulb with lower resistance (the 100W bulb) will consume more power and glow brighter.

Q: Is the current different in the two bulbs since they have different resistances?

No. In a series circuit, there is only one path for the electrons. The current must be exactly the same through all components in series, regardless of their resistance.

Q: What if the bulbs were rated for different voltages?

Then you would have to calculate their exact resistances using $R = \frac{V_{\text{rated}}^2}{P_{\text{rated}}}$ for each bulb separately before comparing them.

Question

A $25	ext{ W}$ and a $100	ext{ W}$ bulb are joined in series and connected to the mains. Which bulb will glow brighter ?

Sigma Percentile · Accepted Answer

### The Brightness Paradox: Why a 25W Bulb Outshines a 100W Bulb in Series

Have you ever looked at a 100W bulb and a 25W bulb and thought, "Obviously, the 100W bulb is brighter"? In a normal household setup, you'd be absolutely right. But physics loves to throw a curveball, and when you connect these two bulbs in **series**, the underdog takes the crown. Let's dive into the fascinating world of electrical power and resistance to understand why the 25W bulb glows brighter.

### Decoding the Wattage Rating

When you buy a bulb, the wattage printed on the box (like 100W or 25W) is its **rated power**. This is the power the bulb will consume *if* it is connected to its rated voltage (usually 220V in India).

The rated power $P$ and the rated voltage $V$ are related to the bulb's internal resistance $R$ by the formula:

$$P = \frac{V^2}{R}$$

Rearranging this, we get the resistance of the bulb:

$$R = \frac{V^2}{P}$$

This equation reveals a crucial secret: **resistance is inversely proportional to rated power**. Because the 25W bulb has a lower rated power than the 100W bulb, it must have a **higher resistance**.

$$R_{25} > R_{100}$$

Think of resistance as a hurdle for the electrons. The 25W bulb is a much bigger hurdle than the 100W bulb.

### The Series Circuit Twist

Now, let's connect these two bulbs in series. In a series circuit, there is only one path for the electrons to flow. This means the **current $i$ must be exactly the same** through both bulbs.

When current flows through a resistor, it dissipates energy in the form of heat and light. The actual power consumed by a component in a circuit is given by Joule's Law:

$$P' = i^2 R$$

Here is where the magic happens. Since the current $i$ is constant for both bulbs, the power they consume is directly proportional to their resistance.

$$P' \propto R$$

### The Final Verdict

We already established that the 25W bulb has a higher resistance ($R_{25} > R_{100}$). Because it has a higher resistance, and the same current is forced through it, it will dissipate more energy.

$$P'_{25} > P'_{100}$$

The 25W bulb consumes more actual power in this specific series setup, and therefore, it glows brighter!

It's a beautiful reminder that in physics, context is everything. A bulb isn't inherently "100 watts bright"—it only consumes 100 watts when given the right conditions. Change the conditions, and the rules of the game change entirely.

Animated Solution for Physics - Current Electricity: A $25 W$ and a $100 W$ bulb are joined in series and connected to the mains. Which bulb will glow brighter ?

Visualized Solution

$S er i es S e t u p$

$R a t e d R es i s t an ce$

$C o m p a r in g R es i s t an ces$

$P o w er in S er i es$

$A c t u a l P o w er C o n s u m e d$

$C o n c l u s i o n$

$T h e W a y F or w a r d$

The Sigma Insight: Ohm's Law, Resistance and Electrical Power

The Brightness Paradox

Decoding the Wattage Rating

The Series Circuit Twist

The Final Verdict

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Animated Solution for Physics - Current Electricity: .math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A 25 W and a 100 W bulb are joined in series and connected to the mains. Which bulb will glow brighter ?