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Physics · 2024 · 3 marks
CBSE 2024 · Region 3 · Set 2 · Q22
A battery of unknown emf E and internal resistance r is connected in a circuit as shown in the figure. When the key ( K ) is open, the voltmeter…
A battery of unknown emf $\displaystyle \mathbf{E}$ and internal resistance $\displaystyle \mathbf{r}$ is connected in a circuit as shown in the figure. When the key ( K ) is open, the voltmeter reads $\displaystyle 10.0$ V and ammeter reads $\displaystyle 0$ A . In the closed circuit, the voltmeter reads $\displaystyle 6.0$ V and ammeter reads $\displaystyle 2.0$ A . Calculate :
(a)
emf of the battery,
(b)
internal resistance of the battery (r), and
(c)
external resistance (R).
Marking-scheme solution
(a) \(\displaystyle \mathrm{V}=\mathrm{E}=10 \mathrm{~V}\) (When key K is open and \(\displaystyle \mathrm{I}=0 \mathrm{~A}\) )
(b) V=E-Ir (When key K is closed and I=$\displaystyle 2$ A)
\[\begin{aligned}
& 6=10-2 \mathrm{r} \\
& \mathrm{r}=2 \Omega
\end{aligned}
\]
(c) \[\begin{gathered}
\mathrm{E}=\mathrm{I}(\mathrm{r}+\mathrm{R}) \\
10=2(2+\mathrm{R}) \\
\mathrm{R}=3 \Omega
\end{gathered}
\]
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