# Why is the lamp with the lower power rating brighter in the series circuit?

If I have two lamps, both of them have different power values, and voltage value is constant , I've been told that the lamp that has less power would be brighter and make more light than the lamp that has a higher power rating in the series circuits.

I searched for the reason but I didn't find an answer.

The 100W bulb is brighter when they are connected in parallel - when they both have the same voltage of 240V across them. But when they are connected in series they have the same current flowing through them; the voltage across each is different. The power dissipated in each bulb is $I^2R$ where $I$ is current and $R$ is resistance. So when the current is the same the bulb with greater resistance emits more light power and is brighter.
Which bulb has more resistance? You can get the resistance of the bulb from the rating using formula $P=\frac{V^2}{R}$. $V$ is the same for both bulbs so the resistances are inversely proportional to the power ratings : $R_{60}/R_{100}=P_{100}/P_{60}=100/60$. The 60W bulb has the higher resistance. Therefore when the same current flows through both (eg when connected in series) the 60W bulb is brighter.
• No. In parallel the voltage across each is the same. In series the current through each is the same. If the same current $I$ passes through the 2 resistors in series, the voltages across them are $V_1=IR_1$ and $V_2=IR_2$. If $R_1 \ne R_2$ then $V_1 \ne V_2$. – sammy gerbil Nov 29 '16 at 18:34