Question

The five identical bulbs in FIGURE $EX28.11$are all glowing. The battery is ideal. What is the order of brightness of the bulbs, from brightest to dimmest? Some may be equal.

A.$P=T>Q=R=S$

B.$P>Q=R=S>T$

C.$P=T>Q>R=S$

D.$P>Q>T>R=S$

Short answer

D.$P>Q>T>R=S$

Step-by-step solution

Given information

We have given that the five identical bulbs in FIGURE $EX28.11$are all glowing.

We need to find that the order of brightness of the bulbs, from brightest to dimmest.

Explanation

The energy is dissipated when the current flows through a resistor. The rate of the dissipated energy is the power. It is given as

$P_R=\frac{{\left(∆V_R\right)}^2}{R}$

The bulbs are identical, so they have the same resistance. Calculating the voltage for each bulb. Bulb $P$is in series with the combination. So, it has the largest voltage which is $\in$.

Both bulbs $S$and $R$are in parallel, Thus they have the same voltage and the same brightness

$S=R$

Bulb $Q$is in parallel with the combination $SRT$, so it has a larger voltage than the other bulbs.

Bulb $T$is in series with the combination $SR$, so it has voltage target than $S$and $R$because the combination $SR$has lesser resistance.

In this case, we rank the brightness by

$P>Q>T>R=S$

Hence, option D is correct.