MHTCET 17 Apr 2026 Shift 2 Paper

Concept:Capacitors in parallel add directly, while capacitors in series follow the reciprocal formula.Explanation:The capacitors $2C$, $3C$, and $4C$ are connected in parallel.For a parallel combination, the equivalent capacitance is the sum of all individual capacitances.$$C_{p} = 2C + 3C + 4C = 9C$$This parallel combination of $9C$ is connected in series with capacitor $C'$.For capacitors in series, the equivalent capacitance is given by:$$\frac{1}{C_{eq}} = \frac{1}{C_{p}} + \frac{1}{C'}$$It is given that the total equivalent capacitance between $A$ and $B$ is $C_{eq} = 6C$.Substitute the known values into the series formula:$$\frac{1}{6C} = \frac{1}{9C} + \frac{1}{C'}$$Rearrange the equation to isolate $\frac{1}{C'}$:$$\frac{1}{C'} = \frac{1}{6C} - \frac{1}{9C}$$Taking LCM of $6C$ and $9C$ as $18C$:$$\frac{1}{C'} = \frac{3 - 2}{18C} = \frac{1}{18C}$$Hence, $C' = 18C$.Answer:The required capacitor $C'$ is $18C$, so the correct option is C.