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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? |
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Answer» (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). |
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