A battery of emf 10 V and internal resistance $3\ \Omega$ is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?
Exercise
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Given,
EMF of battery, $\varepsilon=10\ \text{V}$
Internal resistance of battery, $\text{r}=3\ \Omega$
Current flowing in the circuit, $\text{I}=0.5\text{A}$
Using the forlmula $\text{I}=\frac{\varepsilon}{\text{R}+\text{r}}$
$\text{or}\ \ \text{R}=\frac{\varepsilon}{\text{I}}-\text{r}$
where, R is the external resistance.
$\therefore\ \ \text{R}=\frac{10}{0.5}-3=17\ \Omega$ is the required resistance.
Terminal voltage,
$\text{V}=\text{IR}$
$=0.5\times17$
$=8.5\ \text{V}$
EMF of battery, $\varepsilon=10\ \text{V}$
Internal resistance of battery, $\text{r}=3\ \Omega$
Current flowing in the circuit, $\text{I}=0.5\text{A}$
Using the forlmula $\text{I}=\frac{\varepsilon}{\text{R}+\text{r}}$
$\text{or}\ \ \text{R}=\frac{\varepsilon}{\text{I}}-\text{r}$
where, R is the external resistance.
$\therefore\ \ \text{R}=\frac{10}{0.5}-3=17\ \Omega$ is the required resistance.
Terminal voltage,
$\text{V}=\text{IR}$
$=0.5\times17$
$=8.5\ \text{V}$
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