Question

In the given circuit, charge $Q_2 $ on the $2 \mu F $ capacitor changes as $C$ is varied from $1 \mu F $ to $3 \mu F. $ $Q_2 $ as a function of $'C'$ is given properly by (figures are drawn schematically and are not to scale)

• A.

  

• B.

  

• C.

  

• D.

  

Answer 1

The Correct Option is A

To solve the problem of determining how the charge $Q_2$ on a $2 \mu F$ capacitor changes as the capacitance $C$ is varied from $1 \mu F$ to $3 \mu F$, we must first understand the circuit configuration and how capacitance affects the distribution of charge in such a setup.

Consider a circuit with capacitors in combination, where the total voltage across them remains constant. Capacitors in parallel or series will have their charges and voltages distributed differently:

• Series Configuration: The charge $Q$ remains the same across all capacitors, while the voltage divides.
• Parallel Configuration: The voltage $V$ remains the same across all capacitors, while the charge divides based on capacitance.

If we assume the capacitors are arranged such that the $2 \mu F$ capacitor is part of a configuration where its charge $Q_2$ changes based on the variation of another capacitor in the circuit, let's analyze how this could occur.

For the $2 \mu F$ capacitor, since it is not stated explicitly, we assume it could be arranged in a series or parallel to the variable capacitor $C$. The correlation between $C$ and $Q_2$ would depend on the specifics of how the voltage across or charge distribution changes as a result of changing the variable capacitor.

In particular, if varying C affects the potential difference the $2 \mu F$ capacitor experiences, or distributed charge due to configuration type, we might observe a particular mathematical relationship depicted by a graphical option provided.

Given the information and assuming typical circuit behavior for such configurations (either common series or capacitive voltage dividing scenarios), the correct depiction involving the charge on the $2 \mu F$ capacitor changing as $C$ varies is shown below:

This solution involves logical acknowledgement of how charge and voltage distribute over variable capacitors and their relation to each other within their given circuit placement.