Question

12. Two coils have a combined resistance of 25 Ω when connected in series and a resistance of 4Ω when connected in parallel. What is the resistance of each coil? (5 Ω, 20 Ω)

Answer 1

$\huge\mathfrak\pink{Answer}$

» Given:

•Combined resistance =

In series = 25Ω

In parallel = 4Ω

» We know that,

In series connection,

${\pink{\boxed{R_{eq} = R_1 + R_2}}}$

In parallel connection,

${\pink{\boxed{R _ {eq} = \frac{1}{R_1} + \frac{1}{R_2} }}}$

» Assume

first resistance as $R_1$

second resistance as $R _2$

» By putting values -

25 = $R_1+R_2$....(1)

4 = $\frac{1}{R_1}+\frac{1}{R_2}$....(2)

$R_2 = 25- R_1$..(3)

by putting the value in equation 2

4 = $\frac{1} {R_1} + \frac{1}{25 -R_1}$

$= \frac{25-R_1+R_1}{25R_1 - (R_1)^2}$

$4= \frac{25}{25R_1 - (R_1)^2}$

by cross multiplication

$4(25R_1-(R_1)^2) = 25\\ \\ \\ = 4R_1(25-R_1) = 25$

25 = 5×5

so, one of them should be equal to 5

$25-R_1 = 5\\ \\ \\</p><p>-R_1 = -20$

${\purple{\boxed{R_1 = 20 Ω}}}$

$R_1+R_2 = 25\\ \\ \\</p><p>20+R_2 = 25\\ \\ \\</p><p>{\purple{\boxed{R_2 = 5 Ω}}}$