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Standard XII

Physics

Mixed Combination of Cells

n identical c...

Question

n identical cells each of emf"e" and internal "r" are connected in series to a resistor "R" . deduce an expression for the internal resistance"r "of one cell in terms of current "I" flowing through the circuit?

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Solution

$Total emf of the cells = n ε T otal resistance of the cells = n r External resistance = R Total resistance of the circuit = n r + R Now, according to ohms law . Current in the circuit is given by I = \frac{n ε}{n r + R} \Rightarrow I n r + I R = n ε \Rightarrow I n r + V = n ε \Rightarrow I n r = n ε - V \Rightarrow r = \frac{n ε - V}{I n}$

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n identical cells each of emf"e" and internal "r" are connected in series to a resistor "R" . deduce an expression for the internal resistance"r "of one cell in terms of current "I" flowing through the circuit?

Total emf of the cells=nεTotal resistance of the cells=nrExternal resistance=RTotal resistance of the circuit=nr+RNow, according to ohms law. Current in the circuit is given byI=nεnr+R⇒Inr+IR=nε⇒Inr+V=nε⇒Inr=nε-V⇒r=nε-VIn