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  4. Two resistances R1 and R2 have effective resistance Rs when connected in series and Rp, when connected in parallel. If Rs Rp=16 and R1/R2=4, calculate the values of R1and R2 (in units of resistance).

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Q. Two resistances $R_1$ and $R_2$ have effective resistance $R_s$ when connected in series and $R_p$, when connected in parallel. If $R_s R_p=16$ and $R_1/R_2=4$, calculate the values of $R_1$and $R_2$ (in units of resistance).

KCETKCET 1997Current Electricity

Solution:

In series $R_s = R_1 + R_2$ In parallel $R_p = \frac{R_1R_2}{R_1 + R_2}$
Here, $R_1 4 \, R_2$ (given) and $R_sR_p$ = 16 (given)
But $R_s R_p = ( R_1 + R_2) \frac{R_1R_2}{R_1 +R_2} = R_1R_2$ = 16
$i.e.$ $4R_2 \times R_2$ = 16 $i.e.$ $R_2 = 2 \, \Omega$ and $R_1 = 8 \, \Omega$