An infinite ladder is constructed by connecting several sections of` 2muF,4muF` capacitor combinations as shown in figure . It is terminated by a capacitor of capacitance C . What value should be chosen for C, such that the equivalent capacitance of the number of sections in between ?

Explanation

To solve the problem of finding the value of capacitance \( C \) that should be chosen to terminate the infinite ladder of capacitors, we can follow these steps:

### Step 1: Understand the Configuration
The infinite ladder consists of sections of capacitors \( 2 \, \mu F \) and \( 4 \, \mu F \). The last section is terminated by a capacitor \( C \).

### Step 2: Identify the Equivalent Capacitance
Let the equivalent capacitance of the entire ladder be \( C \). The first section of the ladder consists of a \( 4 \, \mu F \) capacitor in series with the capacitor \( C \). The formula for capacitors in series is:

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