SATHEE: Current Electricity 2 Question 25

Current Electricity 2 Question 25

25. Find the $emf (V)$ and internal resistance $(r)$ of a single battery which is equivalent to a parallel combination of two batteries of emfs $V_{1}$ and $V_{2}$ and internal resistances $r_{1}$ and $r_{2}$ respectively, with polarities as shown in figure

(1997C, 5M)

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Solution:

(a) Equivalent emf $(V)$ of the battery

PD across the terminals of the battery is equal to its emf when current drawn from the battery is zero. In the given circuit,

Current in the internal circuit,

$i = \frac{Net emf}{Total resistance} = \frac{V_{1} + V_{2}}{r_{1} + r_{2}}$

Therefore, potential difference between $A$ and $B$ would be

$\begin{aligned} V_{A} - V_{B} = V_{1} - i r_{1} \\ ∴ & V_{A} - V_{B} = V_{1} - \frac{V_{1} + V_{2}}{r_{1} + r_{2}} r_{1} = \frac{V_{1} r_{2} - V_{2} r_{1}}{r_{1} + r_{2}} \end{aligned}$

So, the equivalent emf of the battery is

$V = \frac{V_{1} r_{2} - V_{2} r_{1}}{r_{1} + r_{2}}$

Note that if $V_{1} r_{2} = V_{2} r_{1} : V = 0$ .

If $V_{1} r_{2} > V_{2} r_{1} : V_{A} - V_{B} =$ Positive i.e. $A$ side of the equivalent battery will become the positive terminal and vice-versa.

(b) Internal resistance ( $r$ ) of the battery

$r_{1}$ and $r_{2}$ are in parallel. Therefore, the internal resistance $r$ will be given by

$1 / r = 1 / r_{1} + 1 / r_{2} or r = \frac{r_{1} r_{2}}{r_{1} + r_{2}}$

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Current Electricity 2 Question 25

25. Find the $emf (V)$ and internal resistance $(r)$ of a single battery which is equivalent to a parallel combination of two batteries of emfs $V_{1}$ and $V_{2}$ and internal resistances $r_{1}$ and $r_{2}$ respectively, with polarities as shown in figure

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Current Electricity 2 Question 25

25. Find the emf(V) and internal resistance (r) of a single battery which is equivalent to a parallel combination of two batteries of emfs V1 and V2 and internal resistances r1 and r2 respectively, with polarities as shown in figure

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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25. Find the $emf (V)$ and internal resistance $(r)$ of a single battery which is equivalent to a parallel combination of two batteries of emfs $V_{1}$ and $V_{2}$ and internal resistances $r_{1}$ and $r_{2}$ respectively, with polarities as shown in figure