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Question:
When a current of $2\,A$ flows in a battery from negative to positive terminal, the potential difference across it is $12 \,V$. If a current of $3\,A$ flowing in the opposite direction produces a potential difference of $15\, V$, the emf of the battery is
When a current of $2\,A$ flows in a battery from negative to positive terminal, the potential difference across it is $12 \,V$. If a current of $3\,A$ flowing in the opposite direction produces a potential difference of $15\, V$, the emf of the battery is
Updated On: Aug 1, 2022
- $12.6\,V$
- $13.2\,V$
- $13.5\,V$
- $14.0\,V$
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The Correct Option is B
Solution and Explanation
Let $\varepsilon$ be emf and $r$ be internal resistance of the battery.
In first case,
$12 = \varepsilon - 2r \quad ...(i)$
In second case,
$15 = \varepsilon + 3r \quad...(ii)$
Subtract $(i)$ from $(ii)$, we get
$r = \frac{3}{5} \Omega$
Putting this value of $r$ in eqn. $(i)$, we get
$\varepsilon = 12 + \frac{2\times 3}{5} $
$ = \frac{60+6}{5}$
$= \frac{66}{5} = 13.2\,V$
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Concepts Used:
Cells
- A device that converts chemical energy into electrical energy is called an electric cell. To an electric circuit, the battery provides the constant electromotive force.
- Each cell comprises 2 half cells which are connected in series by a conductive electrolyte containing anions and cations:
- One-half cell is made up of electrolyte and a negative electrode called an anion.
- The other half cell is made up of electrolytes and a positive electrode called a cathode.
- Redox reactions take place simultaneously.
- While charging, cations are reduced at the cathode, and anions are oxidized at the anode.
- Electrodes do not join each other as they are electrically connected by the electrolyte.
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