Question

Two electric bulbs rated P₁ and P₂ watt at V volt are connected in series across V volt mains ,then their total power consumption P is 1) (P₁+P₂) 2)√P₁ P₂ 3)P₁P₂ /( P₁+P₂ ) 4)(P_{1 +} P₂ )/P₁ P_2. Give reasons.

Answer 1

$$\begin{gathered} R_1=V^2/p_1 \\ {R}_2=V^2/p_2 \\ R=R_1+R_2 \\ I=V/R=V/R_1+R_2 \\ p=I^2(R_1+R_2) \\ p=\frac{V^2}{{\left(R_1+R_2\right)}^2}{R}_1+R_2=\frac{V^2}{{\left(R_1+R_2\right)}^{}}=\frac{1}{{\displaystyle \frac{R_1}{V^2}}+{\displaystyle \frac{R_2}{V^2}}}=\frac{1}{{\displaystyle \frac{1}{p_1}}+{\displaystyle \frac{1}{p_2}}} \\ p=\frac{p_1{p}_2}{p_1+p_2} \end{gathered}$$