In a series combination of three capacitors with capacitances $C$, $2C$, and $3C$ connected to a battery, what is the charge $Q$ on the first capacitor if the voltage across the first capacitor is $\Delta V_1$? Express $Q$ in terms of $C$ and $\Delta V_1$.

Learning Goal: To understand how to calculate capacitance, voltage, and charge for a combination of capacitors connected in series. Consider the combination of capacitors shown in the figure. Three ca...

Learning Goal: To understand how to calculate capacitance, voltage, and charge for a combination of capacitors connected in series. Consider the combination of capacitors shown in the figure. Three capacitors are connected to each other in series, and then to the battery. The values of the capacitances are C, 2C, and 3C, and the applied voltage is ΔV. Initially, all of the capacitors are completely discharged; after the battery is connected, the charge on plate 1 is Q.

In a series combination of three capacitors with capacitances $C$, $2C$, and $3C$ connected to a bat...

Answer

For the first capacitor, the charge and voltage are related by $Q = C\,\Delta V_1$. Since the first capacitor has capacitance $C$, the charge on it is $Q = C\Delta V_1$.

Explanation

What the question is really asking

You are not being asked to use the whole series network yet. You only need the basic charge-voltage-capacitance relationship for the first capacitor.

Using the capacitor definition on capacitor 1

For any capacitor, $$Q = C\,\Delta V.$$

Here, capacitor 1 has capacitance $C$ and the voltage across it is given as $\Delta V_1$. Substituting: $$Q = C\,\Delta V_1.$$

Quick check

Units match: $C$ (farads) times $\Delta V_1$ (volts) gives coulombs, so the expression is consistent.

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In a series combination of three capacitors with capacitances $C$, $2C$, and $3C$ connected to a battery, what is the charge $Q$ on the first capacitor if the voltage across the first capacitor is $\Delta V_1$? Express $Q$ in terms of $C$ and $\Delta V_1$.

What the question is really asking

Using the capacitor definition on capacitor 1

Quick check

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