Question

Cap-monster maze.In Fig. 27-22, all the capacitors have a capacitance of$\mathbf{60}\mathbf{}\mathbf{\mu C}$, and all the batteries have an emf of 10 V. What is the charge on capacitor C? (If you can find the proper loop through this maze, you can answer the question with a few seconds of mental calculation).

Short answer

The charge on capacitor C is$60\mathrm{\mu C}$.

Step-by-step solution

Step 1: Given

$$\begin{gathered} \mathrm{V}=10\mathrm{V} \\ \mathrm{C}=6.0\mathrm{\mu F} \end{gathered}$$

Determining the concept

Here, use the formula for the charge in terms of the voltage and the capacitor. When the capacitors are connected in series with battery, voltage remains same through the capacitors.

Formulae are as follow:

$\mathrm{q}=\mathrm{CV}$

Where, C is capacitance,V is potential difference, q is charge

Determining the charge on capacitor C

Consider the loop as shown in figure 27-22 in which the capacitor C is connected in series with the battery shown by the path in red.

So, the voltage across capacitor C is 10 V

Now, the charge is as follow,

$$\begin{gathered} \mathrm{q}=\mathrm{CV} \\ \mathrm{q}=6.0\times 10 \\ \mathrm{q}=60\mathrm{\mu C} \end{gathered}$$

Hence, the charge on capacitor C is$60\mathrm{\mu C}$

Therefore, first find the voltage through the capacitors. From that, find the charge through the capacitors.