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.

Explanation / Answer

Given that resistance R = 5.0 current passing through the resistance R is i = 0.50 A          Emf   acrros the 5.0 is e = 0.50 A * 5.0                                                      = 2.5 V      current across the rsistance R = 11.0                                             i = e / R                                                 = 2.5V / 11.0                                                 = 0.22A             interna resistance is e   = I r                                             r   = 2.5 V / 0.22A                                                  = 1.10    emf   e is i = e / R + r                  0.22 A = e / 11.0 +1.10                      e = 2.66V

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