\(R _1\) ત્રિજ્યાના અલગ કરેલા સંધારકની સંધારકતા \(n\) ગણી વધી જાય છે જ્યારે તેને \(R _2\) ત્રિજ્યા ધરાવતા અને પૃથ્વી સાથે જોડેલા \((grounded)\) સમકેન્દ્રીય ગોળામાં મૂકવામાં આવે છે. તેમની ત્રિજ્યાઆનો ગુણોત્તર \(\left(\frac{R_2}{R_1}\right) \ldots\) થશે.

A \(\frac{ n }{ n -1}\)
B \(\frac{2 n}{2 n+1}\)
C \(\frac{ n +1}{ n }\)
D \(\frac{2 n+1}{n}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{ n }{ n -1}\)

Step-by-step Solution

Detailed explanation

Capacitance of isolated Conducting sphere \(=4 \pi \varepsilon_{0} R_{1}\) By enclosing inside another sphere of radius \(R_{2}\), new capacitance \(=\frac{4 \pi \varepsilon_{0} R_{1} R_{2}}{\left(R_{2}-R_{1}\right)}\) Given:…

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.

Same subject

Explore more questions on app

From JEE Mains

Explore more questions on app