Question

A resistor 2.5ohm is in series with a reactance j2.5 ohm. The series
combination is supplied with an AC source 50 V. Evaluate the
power dissipated in the circuit.​

Answer 1

$\Large\bf{\color{indigo}GiVeN,}$

• A resistors $\bf{2.5\:\Omega}$ is in series with a resistance $\bf{2.5\:\Omega}$.

• The series combination is supplied with an AC source 50 V.

$\Large\bf{\color{cyan}To\:FiNd,}$

• The power dissipated in the circuit.

$\Large\bf{\color{moccasin}CaLcUlAtIoN,}$

☆ When two resistors are connected in series then the equivalent resistance is,

$\red\bigstar\:\:\bf\green{R_{eq}\:=\:R_1\:+\:R_2\:}$

$\bf\pink{Where,}$

• $\bf{\red{R_1}}\:=\:2.5\:\Omega\:$

• $\bf{\red{R_2}}\:=\:2.5\:\Omega\:$

$\longmapsto\:\:\bf{R_{eq}\:=\:2.5\:+\:2.5\:}$

$\longmapsto\:\:\bf\blue{R_{eq}\:=\:5\:\Omega\:}$

$\bf\orange{We\:know \:that,}$

$\green\bigstar\:\:\bf\purple{Current\:(I)\:=\:\dfrac{Voltage}{R_{eq}}\:}$

$:\longmapsto\:\:\bf{I\:=\:\dfrac{50}{5}\:}$

$:\longmapsto\:\:\bf\pink{I\:=\:10\:A\:}$

$\bf\red{Now,}$

☆ The power dissipated in the circuit is,

$\purple\bigstar\:\:\bf\orange{Power\:(P)\:=\:I^2R\:}$

$:\implies\:\:\bf{Power\:(P)\:=\:(10)^2\times {5}\:}$

$:\implies\:\:\bf{Power\:(P)\:=\:100\times {5}\:}$

$:\implies\:\:\bf\green{Power\:(P)\:=\:500\:W\:}$

$\Large\bold\therefore$ The power dissipated in the circuit is "500W".