Home » Past Questions » Physics » From the diagram above, determine the value of the resistance X

From the diagram above, determine the value of the resistance X


Question

From the diagram above, determine the value of the resistance X

Options

A) 6Ω

B) 9Ω

C) 12Ω

D) 15Ω


The correct answer is D.

Explanation:

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

More Past Questions:


Dicussion (1)

  • 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