એક ગૂંચળાનું આત્મપ્રેરકત્વ L = 0.04 H અને અવરોધ \(R =12 \Omega\) છે, તેને 220 V, 50 Hz ના સપ્લાય સાથે જોડવામાં આવે છે, ત્યારે આ ગૂંચળામાંથી વહેતો વિધુતપ્રવાહ કેટલો હશે ?

A 12.7 A
B 14.7 A
C 11.7 A
D 10.7 A

Verified Solution

Answer & Solution

Correct Answer

(A) 12.7 A

Step-by-step Solution

Detailed explanation

A.12.7 A
ઇન્ડક્ટિવ રિએક્ટન્સ
\(\begin{aligned} X _{ L }=\omega L =2 \pi \nu L \\ X _{ L } =2 \times 3.14 \times 50=0.04 \\ X _{ L } =12.56 \Omega\end{aligned}\)
⇒ પરિપથનો ઇમ્પિકન્સ
\(Z=\sqrt{R^2+\left(X_L\right)^2}\)
\(=\sqrt{(12)^2+(12.56)^2}\)
\(=17.37 \Omega\)
⇒ ગૂંચળામાંથી વહેતો વિધુતપ્રવાહ
\(\begin{array}{l}I=\frac{V}{Z} \\ I=\frac{220}{17.37} \\ I \approx 12.7 A\end{array}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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