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# 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 resistance of the resistor ? What is the terminal voltage of the battery when the circuit is closed ?

$\begin{array}{1 1} 8.5\Omega \\ 7.2\;\Omega \\ 8.3\;\Omega \\ 2.3\;\Omega \end{array}$

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A)
Solution :
$E= 10\;V$
$r= 3 \Omega$
$I= 0.5\;A$
$I= \large\frac{E}{R+r}$
=> $R+r= \large\frac{E}{I}$
=> $\large\frac{10}{0.5}$$=20$
$\therefore R= 20-3$
$\qquad=> 17 \; \Omega$
Terminal voltage $V= IR$
$\quad=> 0.5 \times 17$
$\quad=> 8.5\;\Omega$
Answer : $8.5\Omega$