Two metal spheres of radii $r_1$ and $r_2$ having charges $q_1$ and $q_2$ are brought in contact. Which statement is NOT correct?
Show Hint
- Total charge is conserved
- Both spheres attain same potential
- Final potential is $\frac{1}{4\pi\epsilon_0}\frac{(q_1+q_2)}{(r_1+r_2)}$
- Final potential is $\frac{1}{4\pi\epsilon_0}\frac{(q_1+q_2)(r_1+r_2)}{r_1 r_2}$
The Correct Option is C
Solution and Explanation
Step 1: Condition of equilibrium \[ V_1 = V_2 \Rightarrow \frac{q'_1}{r_1} = \frac{q'_2}{r_2} \]
Step 2: Total charge conservation \[ q'_1 + q'_2 = q_1 + q_2 \]
Step 3: Final potential Common potential: \[ V = \frac{1}{4\pi\epsilon_0}\frac{q_1+q_2}{r_1 + r_2 \text{ (incorrect assumption)}} \] This is WRONG because potential depends on individual radii, not sum. Correct derivation gives: \[ V = \frac{1}{4\pi\epsilon_0}\frac{q_1+q_2}{\frac{r_1 r_2}{r_1 + r_2}} \] So option (C) is incorrect. Final Answer: \[ \boxed{(C)} \]
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A circuit consisting of a capacitor C, a resistor of resistance R and an ideal battery of emf V, as shown in figure is known as RC series circuit.
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