Question

A 4Ω, 6Ω, 10Ω & 15Ω are connected in parallel, which resistor will consume the most power?

Answer 1

Gives

$R_1=4\Omega\\R_2=6\Omega\\R_3=10\Omega\\R_4=15\Omega$

R₁ and R₂ net resistance R'₁

$R_1'=\frac{R_1R_2}{R_1+R_2}=\frac{4\times6}{4+6}=\frac{24}{10}=\frac{12}{5}\Omega$

R₃ and R₄ net resistance R'₂

$R'_2=\frac{R_3R_4}{R_3+R_4}=\frac{10\times15}{10+15}=\frac{150}{25}=6\Omega$

$R_{net}=\frac{R'_1R'_2}{R'_1+R'_2}=\frac{\frac{12}{5}\times6}{\frac{12}{5}+6}=1.71\Omega$

$P=IV$

Potential is same all resistance

Then P high ,I High

4 ohm resistance Power maximum

$P_{max}=IV$

$P_{max}=I^2R=4I^2 watt$