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Chapter 14: Problem 25

Five cells, each of EMF \(E\) and internal resistance \(r\) are connected in series. If due to oversight, one cell is connected wrongly, then the equivalent EMF and internal resistance of the combination, is (A) \(5 E\) and \(5 r\) (B) \(3 E\) and \(3 r\) (C) \(3 E\) and \(5 r\) (D) \(5 E\) and \(3 r\)

Short Answer

Expert verified
The equivalent EMF and internal resistance of the combination are: \(3 E\) and \(5 r\) So, the correct answer is (C) \(3 E\) and \(5 r\).

Step by step solution

01

Understand the connections

In this problem, we have five cells connected in series, but one cell is connected wrongly. Let's consider the correct connection as positive (+) and the wrong connection as negative (-). So, we have four cells with positive EMF and one cell with negative EMF.
02

Calculate total EMF

When cells are connected in series, their EMFs add up. So, we have four cells with EMF \(E\) and one cell with EMF \(-E\). Therefore, the total EMF of the combination is: Total EMF = \(4 \times E + (-E)\) Total EMF = \(3E\)
03

Calculate total internal resistance

Now, let's look at the internal resistance of each cell. The internal resistance of each cell is \(r\), and they are also connected in series. In series connection, the resistances add up. In this case, all five cells have the same internal resistance \(r\), so the total internal resistance of the combination is: Total internal resistance = \(5 \times r\) Total internal resistance = \(5r\)
04

Find the answer

Now, we have the total EMF and the total internal resistance of the combination. So, the equivalent EMF is \(3E\) and the equivalent internal resistance is \(5r\). From the given options, the correct answer is: (C) \(3 E\) and \(5 r\)

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Most popular questions from this chapter

This question has statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-I: Higher the range, greater is the resistance of ammeter. Statement-II: To increase the range of ammeter, additional shunt needs to be used across it. (A) Statement-I is true, Statement-II is true, Statement-II is not the correct explanation of Statement-I. (B) Statement-I is true, Statement-II is false. (C) Statement-I is false, Statement-II is true. (D) Statement-I is true, Statement-II is true, Statement-II is correct explanation of Statement-I.

A dielectric slab of thickness \(d\) is inserted in a parallel plate capacitor whose negative plate is at \(x=0\) and positive plate is at \(x=3 d\). The slab is equidistant from the plates. The capacitor is given some charge. As \(x\) goes from 0 to \(3 d\), (A) the magnitude of the electric field remains the same. (B) the direction of the electric field remains the same. (C) the electric potential increases continuously. (D) the electric potential increases at first, then decreases and again increases.

Two cells with the same EMF \(E\) and different internal resistances \(r_{1}\) and \(r_{2}\) are connected in series to an external resistance \(R\). The value of \(R\) for the potential difference across the first cell to be zero is (A) \(\sqrt{r_{1} r_{2}}\) (B) \(r_{1}+r_{2}\) (C) \(r_{1}-r_{2}\) (D) \(\frac{r_{1}+r_{2}}{2}\)

A voltmeter and an ammeter are connected in series to an ideal cell of EMF \(E\). The voltmeter reading is \(V\), and the ammeter reading is \(I .\) (A) \(V

A galvanometer of resistance \(400 \Omega\) can measure a current of \(1 \mathrm{~mA}\). To convert it into a voltmeter of range \(8 \mathrm{~V}\), the required resistance is (A) \(4600 \Omega\) (B) \(5600 \Omega\) (C) \(6600 \Omega\) (D) \(7600 \Omega\)
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