Question

A battery of emf 10v and internal resistance 3 ohms is connected to a resistor. if the current in the circuit is 0.5 a , find the resistance of the resistor and terminal voltage of battery

Answer 1

The resistance of the battery is 17 ohms and the voltage is 8.5 V

Explanation:

• emf of battery=10 v
• Internal resistance of battery "r" =3 ohms
• Current in the circuit "I" = 0.5 A
• Resistance of the resistor = R

• According to Ohm's law

I = E/(R+r)

R=17 ohms

Terminal voltage of the resistor = V

Ohm's law states that

V=I x R

V = 0.5 x 17

V= 8.5 V

Thus the resistance of the battery is 17 ohms and the voltage is 8.5 V

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Answer 2

Explanation:

$\Large{\red{\underline{\underline{\tt{\blue{Solution:}}}}}}$

 ‎ ‎ ‎ ‎ ‎ ‎ ‎

$\longrightarrow$ Emf of batter, $\sf E\:=\:10V$

$\longrightarrow$ Internal resistance of the battery, $\sf r\:=\:3\Omega$

$\longrightarrow$ Current in the circuit, $\sf I\:=\:0.5\,A$

$\longrightarrow$ Resistance of the resistor = $\sf{R}$

 ‎ ‎ ‎ ‎ ‎ ‎ ‎

 ‎ ‎ ‎ ‎ ‎ ‎ ‎

The relation for current using ohm's law is

 ‎ ‎ ‎ ‎ ‎ ‎ ‎

$\boxed{\sf{\pink{I\:=\: \dfrac{E}{R+r}}}}$

 ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎

$\leadsto$ $\sf R+r\:=\: \dfrac{E}{I}$

 ‎ ‎ ‎ ‎ ‎ ‎ ‎

$\leadsto$ $\sf R+r\:=\: \dfrac{10}{0.5}$

 ‎ ‎ ‎ ‎ ‎ ‎ ‎

$\leadsto$ $\sf R+r\:=\:20\Omega$

 ‎ ‎ ‎ ‎ ‎ ‎ ‎

$\sf \therefore R\:=\:20-3\:=\:17\Omega$

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According to Ohm's Law

 ‎ ‎ ‎ ‎ ‎ ‎

$\hookrightarrow$ $\sf V\:=\:I\,R$

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$\sf V\:=\:0.5\times 17$

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$\sf V\:=\:8.5\,V$

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$\hookrightarrow$ Hence the resistance of the resistors is $\sf{\red{17\Omega}}$ and the terminal voltage is $\sf{\red{8.5V}}$