Question

problem 19.45 part a what is the ratio of the voltage v1 across capacitor c1 in (figure 1) to the voltage v2 across capacitor c2? suppose that c2 = 18 μf. express your answer using two significant figures. v1/v2=

Explanation:

Step1: Recall capacitor - voltage relation

For capacitors in series, the charge $Q$ on each capacitor is the same. The charge on a capacitor is given by $Q = CV$. So, for two capacitors $C_1$ and $C_2$ in series, $Q_1=Q_2$, which implies $C_1V_1 = C_2V_2$.

Step2: Solve for the ratio of voltages

From $C_1V_1 = C_2V_2$, we can solve for $\frac{V_1}{V_2}$. Rearranging the equation gives $\frac{V_1}{V_2}=\frac{C_2}{C_1}$.

Step3: Substitute the given values

Given $C_1 = 1.0\ \mu F$ and $C_2 = 18\ \mu F$. Then $\frac{V_1}{V_2}=\frac{18\ \mu F}{1.0\ \mu F}=18$.

Answer:

18