SATHEE: Current Electricity 4 Question 5

Current Electricity 4 Question 5

5. An ideal battery of $4 V$ and resistance $R$ are connected in series in the primary circuit of a potentiometer of length $1 m$ and resistance $5 Ω$ . The value of $R$ to give a potential difference of $5 m V$ across $10 c m$ of potentiometer wire is

(2019 Main, 12 Jan I)

(a) $395 Ω$

(b) $495 Ω$

(d) $480 Ω$

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Solution:

Given, potential difference of $5 m V$ is across $10 m$ length of potentiometer wire. So potential drop per unit length is

$= \frac{5 \times 10^{- 3}}{10 \times 10^{- 2}} = 5 \times 10^{- 2} \frac{V}{m}$

Hence, potential drop across $1 m$ length of potentiometer wire is

$V_{A B} = 5 \times 10^{- 2} \frac{V}{m} \times 1 = 5 \times 10^{- 2} V$

Now, potential drop that must occurs across resistance $R$ is

$V_{R} = 4 - 5 \times 10^{- 2} = \frac{395}{100} V$

Now, circuit current is

$i = \frac{V}{R_{total}} = \frac{4}{R + 5}$

Hence, for resistance $R$ , using $V_{R} = i R$ , we get

$\begin{aligned} \frac{395}{100} & = \frac{4}{R + 5} \times R \\ 395 (R + 5) & = 400 R \\ 395 \times 5 & = (400 - 395) R \end{aligned}$

$\Rightarrow R = 395 Ω$

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Current Electricity 4 Question 5

5. An ideal battery of $4 V$ and resistance $R$ are connected in series in the primary circuit of a potentiometer of length $1 m$ and resistance $5 Ω$ . The value of $R$ to give a potential difference of $5 m V$ across $10 c m$ of potentiometer wire is

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 4 Question 5

5. An ideal battery of 4V and resistance R are connected in series in the primary circuit of a potentiometer of length 1m and resistance 5Ω. The value of R to give a potential difference of 5mV across 10cm of potentiometer wire is

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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5. An ideal battery of $4 V$ and resistance $R$ are connected in series in the primary circuit of a potentiometer of length $1 m$ and resistance $5 Ω$ . The value of $R$ to give a potential difference of $5 m V$ across $10 c m$ of potentiometer wire is