Question

a circuit has two 57.7 ohm resistors in series and a terminal voltage 9.13 v. if the circuit contains only one 10.8 v battery, what is the internal resistance of the battery?

21.1 \\(\omega\\)
18.7 \\(\omega\\)
26.6 \\(\omega\\)
28.0 \\(\omega\\)

Explanation:

Calculate equivalent external resistance

Using the Series and Parallel Circuits knowledge point

$$
LATEXBLOCK0
$$

Determine circuit current

Using the Ohm's Law knowledge point

$$
LATEXBLOCK1
$$

Relate terminal voltage to electromotive force

The terminal voltage \(V_{\text{term}}\) is related to the battery's electromotive force \(\mathcal{E}\) and internal resistance \(r\) by:

$$ V_{\text{term}} = \mathcal{E} - I \cdot r $$

where \(\mathcal{E} = 10.8\text{ V}\).

Solve for internal resistance

We rearrange the equation to isolate the internal resistance \(r\):

$$
LATEXBLOCK2
$$

Comparing this result with the given choices, it matches \(21.1\ \Omega\).

Answer:

• (A) 21.1 \(\Omega\) (Correct answer)
• (B) 18.7 \(\Omega\)
• (C) 26.6 \(\Omega\)
• (D) 28.0 \(\Omega\)