From the diagram above determine the value of t... - JAMB Physics 2002 Question

Let the combined parallel resistance of 3 Ω and x = Q Ω

∴ Total resistance in the circuit = 2 + Q + 1.5 = 3.5 + Q Ω

Total current in the circuit = 2A

P.D a cross the circuit 12 volts

∴ From Ohm’s law, V = IR

12 = 2(3.5 + Q)

= 7.0 + 2Q

∴ 2Q = 12 – 7

= 5

∴ Q = ⁵/₂ = 2.5 Ω

Thus from parallel formula: I/Q = 1/3 + 1/x
¹/_2.5 = ¹/₃ + ¹/_x

∴ ¹/_x = ¹/_2.5 - ¹/₃ = ^3-2.5/_7.5 = ^0.5/_7.5

X = ^7.5/_0.5 = ⁷⁵/₅ = 15 Ω

∴ X = 15 Ω