The effective capacitance of two capacitors of capacitances $$C1$$' and $$C2$$' (with$$ $$C2$$′$$C1$$′$$) connected in parallel is $$25/6$$ times the effective capacitance when they are connected in series. The ratio $$C2$$′$$C1$$′ is :

Question

The effective capacitance of two capacitors of capacitances $$C1$$' and $$C2$$' (with$$ $$C2$$′>$$C1$$′$$) connected in parallel is $$25/6$$ times the effective capacitance when they are connected in series. The ratio $$C2$$′$$C1$$′ is :

Infinity Learn · Accepted Answer

$$C1$$′$$+C2$$′$$=256C1$$′$$C2$$′$$C1$$′$$+C2$$′ ⇒       $$6C1$$′$$+C2$$′$$2=25C1$$′$$C2$$′ ⇒$$6C1$$′$$2+6C2$$′$$2$$−$$13C1$$′$$C2$$′$$=0$$         ...(1) Let                $$C2$$′$$=xC1$$′ eqn. (1) becomes $$6x2$$−$$13x+6=0$$                                                $$x=3/2$$ or $$23$$ Since $$C2$$′>$$C1$$′           $$x=23$$ is not possible.

The effective capacitance of two capacitors of capacitances C₁^' and C₂^' (with ${C_{2}}^{'} > {C_{1}}^{'}$ ) connected in parallel is 25/6 times the effective capacitance when they are connected in series. The ratio $\frac{C_{2}^{'}}{C_{1}^{'}}$ is :

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The effective capacitance of two capacitors of capacitances C1' and C2' (with C2′>C1′) connected in parallel is 25/6 times the effective capacitance when they are connected in series. The ratio C2′C1′ is :

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The effective capacitance of two capacitors of capacitances C₁^' and C₂^' (with ${C_{2}}^{'} > {C_{1}}^{'}$ ) connected in parallel is 25/6 times the effective capacitance when they are connected in series. The ratio $\frac{C_{2}^{'}}{C_{1}^{'}}$ is :