Three resistors are connected as shown in the diagram.

Though the resistor 5 ohm, a current of 1 ampere is flowing.
(i) What is the current through the other two resistors?
(ii) What is the p.d. across AB and across AC?
(iii) What is the total resistance?

Explanation

(a) As current `(I_1)` throught `R_1` is `1 A`,
pd across `R_1`, i.e., `V_1 = I_1 R_1 = 1 xx 5 = 5 V`
Since `R_2` and `R_3` are in parallel, resultant resistance between B and C is given by
`R_p = ("product of" R_2 and R_3)/("sum of" R_2 and R_3) = (10 xx 15)/(10 + 15) Omega = (150)/(25) Omega = 6 Omega`
pd across bC, i.e., `V_2 = I_1 R_p = (1 A)(6 Omega) = 6 V` (as current through BC is `I_1`, i.e., 1 A)
pd across AC = pd across AB + pd across `BC = 5 V + 6 V = 11 V`
(b) Current through `R_2` i.e., `I_2 = (V_2)/(R_2) = (6 V)/(10 Omega) = 0.6 A`
Current through `R_3` i.e., `I_3 = I_1 - I_2 = 1 A - 0.6 A = 0.4 A`
(c) Total resistance between A and C i.e., `R = R_1 + R_p = 5 Omega + 6 Omega = 11 Omega`
(The resultant of `R_2` and `R_3` which are in parallel is `R_p` , and `R_1` and `R_p` are in series).