Answer:
9 Ω
Step-by-step explanation:
The following data were obtained from the question:
Resistor 1 (R1) = 3 Ω
Resistor 2 (R2) = 3 Ω
Resistor 3 (R3) = 3 Ω
Resistor 4 (R4) = 3 Ω
Resistor 5 (R5) = 3 Ω
Resistor 6 (R6) = 3 Ω
Resistor 7 (R7) = 3 Ω
Resistor 8 (R8) = 3 Ω
Resistor 9 (R9) = 3 Ω
Resistor 10 (R10) = 3 Ω
Resistor 11 (R11) = 3 Ω
Resistor 12 (R12) = 3 Ω
Equivalent Resistance (R) =.?
From the above diagram,
Resistor 1, 2, 3, 4, 5 and 6 are in series connection and in parralle connections with Resistor 7, 8, 9, 10, 11 and 12 which are also in series connection.
Thus we shall determine the equivalent resistance of Resistor 1, 2, 3, 4, 5 and 6
This is illustrated below:
Resistance Ra = R1 + R2 + R3 + R4 + R5 + R6
Ra = 3 + 3 + 3 + 3 + 3 + 3
Ra = 18 Ω
Next, we shall determine the equivalent resistance of Resistor 7, 8, 9, 10, 11 and 12.
This is illustrated below:
Resistance Rb = R7 + R8 + R9 + R10 + R11 + R12
Rb = 3 + 3 + 3 + 3 + 3 + 3
Rb = 18 Ω
Thus, Ra and Rb are in parallel connections. The equivalent resistance between A and B can be obtained as shown below :
Ra = 18 Ω
Rb = 18 Ω
Equivalent resistance R =?
1/R = 1/Ra + 1/Rb
1/R = 1/18 + 1/18
1/R = 2/18
1/R = 1/9
Invert
R = 9 Ω
Therefore, the equivalent resistance between A and B is 9 Ω.