Question

The resistance of 8 ohm and inductive reactance of 6 ohm are connected in series in an alternating current circuit. The impedance of circuit will be :

• A. 2 ohm
• B. 14 ohm
• C. 14\(\sqrt{2}\) ohm
• D. 10 ohm

Hint:

This problem uses a 6-8-10 Pythagorean triple, which is a common pattern in physics and math problems. Recognizing this (a multiple of the 3-4-5 triple) can help you find the answer quickly without detailed calculation.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Impedance (Z) is the total opposition to the flow of alternating current in a circuit. In a series R-L circuit, it is the vector sum of the resistance (R) and the inductive reactance (X\(_L\)).
Step 2: Key Formula or Approach:
The formula for the impedance of a series R-L circuit is: \[ Z = \sqrt{R^2 + X_L^2} \] where R is the resistance and X\(_L\) is the inductive reactance.
Step 3: Detailed Explanation:
We are given the following values:
Resistance (R) = 8 \(\Omega\)
Inductive reactance (X\(_L\)) = 6 \(\Omega\)
Substituting these values into the impedance formula: \[ Z = \sqrt{(8)^2 + (6)^2} \] \[ Z = \sqrt{64 + 36} \] \[ Z = \sqrt{100} \] \[ Z = 10 \, \Omega \] Step 4: Final Answer:
The impedance of the circuit is 10 ohm.