Question

three resistors, 11ω, 53ω, and ( r ), are connected in series with a 24.0v battery. the total current flowing through the battery is 0.16a. find the potential difference across resistor ( r ).

a. 14v

b. 56v

c. 1.8v

d. 9.7v

e. 8.5v

Explanation:

Step1: Calculate total resistance

Use Ohm's law $R_{total}=\frac{V}{I}$, where $V = 24.0V$ and $I=0.16A$. So $R_{total}=\frac{24.0}{0.16}=150\Omega$.

Step2: Calculate resistance of $R$

The resistors are in series, so $R_{total}=11 + 53+R$. Then $R=R_{total}-(11 + 53)=150-(11 + 53)=86\Omega$.

Step3: Calculate potential difference across $R$

Use Ohm's law $V_R=IR$, with $I = 0.16A$ and $R = 86\Omega$. So $V_R=0.16\times86 = 13.76\approx14V$.

Answer:

A. 14V