Question

Question:In figure 18.102 suppose that V_C-V_F=8 V and V_D-V_E=4.5 V.

(a) What is the potential difference V_C-V_D?

(b) If the element between the battery C and D is a battery, is the + end of the battery at C or D?

Short answer

The potential difference between C and D is 3.5V.

Step-by-step solution

Identification of given data

The potential difference between C and F is $V_C-V_F=8\text{V}$.

The potential difference between D and E is$V_D-V_E=4.5\text{V}$.

The potential difference between point C and D is found by applying KVL rule in the second loop.

Determination of potential difference between point C and D

Apply Kirchhoff’s voltage rule in second loop to find the potential difference between C and D:

$\left(V_C-V_F\right)-\left(V_D-V_E\right)-\left(V_C-V_D\right)=0$

$\left(V_C-V_D\right)=\left(V_C-V_F\right)-\left(V_D-V_E\right)$

Substitute all the values in above equation.

$$\begin{gathered} V_C-V_D=8\text{V}-4.5\text{V} \\ {V}_C-V_D=3.5\text{V} \end{gathered}$$

Therefore, the potential difference between C and D is $3.5\text{V}$.