SATHEE: current-electricity Question 29

विद्युत् धारा

Question: Q. 3. Two cells of emfs $Misplaced &$ and internal resistances $Misplaced &$ respectively are connected in parallel. Obtain expressions for the equivalent.

(i) resistance and

(ii) emf of the combination U [CBSE Comptt. 2018]

Sol. Obtaining Expression for the equivalent

(i) resistance

(ii) emf

$\begin{aligned} \frac{1}{r} & = \frac{1}{r_{1}} + \frac{1}{r_{2}} ∴ & r & = \frac{r_{1} r_{2}}{r_{1} + r_{2}} I & = I_{1} + I_{2} V & = E_{1} - I_{1} r_{1} and V = E_{2} - I_{2} r_{2} ∴ & I & = (\frac{E_{1} - V}{r_{1}}) + (\frac{E_{2} - V}{r_{2}}) also & V & = E_{e q} - I r_{e q} (i) & r_{e q} & = \frac{r_{1} r_{2}}{r_{1} + r_{2}} (ii) & E_{e q} & = \frac{E_{1} r_{2} + E_{2} r_{1}}{r_{1} + r_{2}}) - I (\frac{r_{1} r_{2}}{r_{1} + r_{2}}) & [CBSE Marking Scheme 2018] \end{aligned}$

Q. 4. First a set of n equal resistors of $R$ each is connected in series to a battery of emf $E$ and internal resistance $R$ . A current $I$ is observed to flow. Then the $n$ resistors are connected in parallel to the same battery. It is observed that the current becomes 10 times. What is $n$ ?

A [SQP I 2017]

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Solution:

Ans.

$\begin{aligned} I = \frac{E}{(R + n R)} & 10 I = \frac{E}{R + \frac{R}{n}} & \frac{1 + n}{(1 + \frac{1}{n})} = 10 \Rightarrow \frac{1 + n}{(n + 1)} n = 10 & n = 10 \end{aligned}$

[CBSE Marking Scheme 2017]

Detailed Answer :

It is observed that an equivalent resistance of series combination is in series with internal resistance of a battery. Equivalent resistance of parallel combination will also be in series with internal resistance of battery.

Hence in series combination of resistors, current $I$ will be :

$\begin{matrix} (i) & I = \frac{E}{(R + n R)} \end{matrix}$

In case of parallel combination, current $10 I$ will be :

$\begin{matrix} (ii) & \frac{E}{(R + \frac{R}{n})} = 10 I \end{matrix}$

From the equations (i) and (ii),

$\frac{1 + n}{(1 + \frac{1}{n})} = 10$

$\begin{array}{ll} So, & 10 = \frac{1 + n}{(n + 1)} n Hence, & n = 10 \end{array}$

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Detailed Answer :

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विद्युत् धारा

Detailed Answer :

विषयसूची

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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