Three resistors each of resistance 10 ohm are connected, in turn, to obtain (i) minimum resistance (ii) maximum resistance. Complete (a) The effective resistance in each case (b) ratio of minimum to maximum resistance so obtained.

Explanation

Given, Resistance of each resistor `R = 10 Omega` no. of resistor, n = 3
(i) If three resistors are connected in parallel, we get minimum resistance.
`:.` Minimum resistance `R_("min") = R_(P) = (R )/(n) = (10)/(3) Omega = 3.33 Omega`
(ii) If three resistors are connected in series, we get maximum resistance.
`:.` Maximum resistance `R_("max") = R_(s) = n R = 3 xx 10 = 30 Omega`
The effective resistance to get maximum resistance
`R_(eff) = nR = 3 xx 10 = 30 Omega` (in series)
(b) `(R_("min"))/(R_("max")) = (((10)/(3)))/((3 xx 10)) = (10)/(90) :. (R_("min"))/(R_("max")) = (1)/(9)`.