Question

Calculate the resultant resistance in the following circuit.

• A. 3 $\Omega$
• B. 10 $\Omega$
• C. 13 $\Omega$
• D. 7 $\Omega$

Hint:

For resistors in series, add their resistances directly. For parallel resistors, use the reciprocal formula.

Answer 1

The Correct Option is B

In this circuit, we have a combination of resistors. The 4 $\Omega$ and 7 $\Omega$ resistors are in series, so their total resistance is: \[ R_1 = 4 \, \Omega + 7 \, \Omega = 11 \, \Omega \] Now, this combination is in parallel with the 12 $\Omega$ resistor. The total resistance for resistors in parallel is given by: \[ \frac{1}{R} = \frac{1}{R_1} + \frac{1}{12 \, \Omega} \] \[ \frac{1}{R} = \frac{1}{11 \, \Omega} + \frac{1}{12 \, \Omega} \Rightarrow R = 10 \, \Omega \] Thus, the resultant resistance is 10 $\Omega$.