A battery has emf epsilon and internal resistance r. When a 5.0-Ohm resistor is

Question

A battery has emf epsilon and internal resistance r. When a 5.0-Ohm resistor is connected across the terminals, the current is 0.50 A. When this resistor is replaced by an 11.0-Ohm resistor, the current is 0.25 A. Find the emf epsilon and the internal resistance r. A galvanometer of resistance 100 Ohm gives a full-scale reading when its current is 0.1 mA. It is to be used in a multi-range voltmeter as shown in Figure 20-53, where the connection refer to full-scale readings. Determine R1, R2 and R3. The galvanometer of Problem 4 is to be used in a multi-range ammeter with the full-scale readings indicated in Figure 20-57. Determine R1, R2, and R3 Figure 20-54 In this problem, you are to derive a relation between the

Explanation / Answer

Data: Resistance of galvanometer, Rg = 100 Full scale current reading, ig = 0.1 mA                                            = 1 x 10^-4 A Solution: For connection of 1 V: V = ig ( Rg + R1 ) 1 = 1 x 10^-4 * ( Rg + R1 ) Rg + R1 = 10^4 R1 = 10^4 - 100      = 9900 For connection of 10 V: For connection of 10 V: V = ig ( Rg + R1 + R2 ) 10 = 1 x 10^-4 * ( Rg + R1 + R2 ) Rg + R1 + R2 = 10^5 R2 = 10^5 - 100 - 9900      = 90000 For connection of 100 V: V = ig ( Rg + R1 ) 100 = 1 x 10^-4 * ( Rg + R1 + R2 + R3 ) Rg + R1 + R2 + R3= 10^6 R3 = 10^6 - 100 - 9900 - 90000      = 900000 Ans: R1 = 9900 R2 = 90000 R3 = 900000 V = ig ( Rg + R1 + R2 ) 10 = 1 x 10^-4 * ( Rg + R1 + R2 ) Rg + R1 + R2 = 10^5 R2 = 10^5 - 100 - 9900      = 90000 For connection of 100 V: V = ig ( Rg + R1 ) 100 = 1 x 10^-4 * ( Rg + R1 + R2 + R3 ) Rg + R1 + R2 + R3= 10^6 R3 = 10^6 - 100 - 9900 - 90000      = 900000 Ans: R1 = 9900 R2 = 90000 R3 = 900000 For connection of 100 V: For connection of 100 V: V = ig ( Rg + R1 ) 100 = 1 x 10^-4 * ( Rg + R1 + R2 + R3 ) Rg + R1 + R2 + R3= 10^6 R3 = 10^6 - 100 - 9900 - 90000      = 900000 Ans: R1 = 9900 R2 = 90000 R3 = 900000 V = ig ( Rg + R1 ) 100 = 1 x 10^-4 * ( Rg + R1 + R2 + R3 ) Rg + R1 + R2 + R3= 10^6 R3 = 10^6 - 100 - 9900 - 90000      = 900000 Ans: R1 = 9900 R2 = 90000 R3 = 900000

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