Question

3 resistances of 2 ohm, 3 ohm and 6 ohm are connected (i) in series (ii) in parallel. Calculate the ratio of the effective resistance of series and parallel combination of resistances

Answer 1

Rs= R1+R2+R3

2+3+6=11ohm( effective resistance in series)


1/To=1/R1+1/R2+1/R3

1/2+1/3+1/6

6/12+4/12+2/12

=12/12=1ohm(effective resistance in parallel)

Answer 2

Answer:

(i) resistance in series

$r_{s} = r_{1} + r_{2} + r_{3}....... \\ r_{s} = 2 \: ohm \: + 3 \: ohm \: + \: 6 \: ohm \\ r_{s} = 11 \: ohm$

(ii) resistance in series

$\frac{1}{ r_{p} } = \frac{1}{ r_{1} } + \frac{1}{ r_{2} } + \frac{1}{ r_{3}} ....... \\ \frac{1}{ r_{p} } = \frac{1}{2} + \frac{1}{3} + \frac{1}{6} \\ \frac{1}{ r_{p} } = \frac{6}{12} + \frac{4}{12} + \frac{2}{12} \\ \frac{1}{ r_{p} } = \frac{12}{12} = 1 \: ohm$

ratio of resistance in series and parallel:

Rs : Rp :: 11 ohm : 1 ohm