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Chapter 4: Q61P (page 845)

Question: The potential difference across the terminals of a battery is 840 V when there is a current of 1.50 A in the battery from the negative to the positive terminal. When the current is 3.50 A in the reverse direction, the potential difference becomes 10.20 V . (a) What is the internal resistance of the battery? (b) What is the emf of the battery?

Short Answer

Expert verified

Answer

  1. The internal resistance of the battery is0.36Ω .
  2. The emf of the battery is 8.94 V .

Step by step solution

01

Define the ohm’s Law.

Consider the real source of emf has internal energy then its terminal potential difference is as follows:

Vab=ε-IR ….. (1)

02

Determine the internal resistance.

(a)

Consider the given expression for the current and the voltage.

Vba=8.40VIba=1.5A

Substitute the values in the equation (1).

8.40=ε-1.5rε=8.40+1.5r

Consider the current is in the reverse direction, the potential difference becomes .

Substitute the values in the equation V=ε+Irand solve.

10.20=8.30+1.5r+3.5r5r=1.8r=0.36Ω

Hence, the internal resistance of the battery is 0.36 .

03

Determine the emf of battery.

(b)

Given: the value of the internal resistance is 0.36Ω.

Substitute for in the equationε=8.40+1.5r .

ε=8.40+1.5×0.36=8.94V

Hence, the emf of the battery is 8.94 V.

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