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A real battery with sigma = 1.5 V and internal resistance r = 0.5 ohm is connect

ID: 1525951 • Letter: A

Question

A real battery with sigma = 1.5 V and internal resistance r = 0.5 ohm is connected to a load with R = 2 ohm. (a) hat is the terminal voltage of the battery? (b) Suppose two such identical batteries are connected in series to the same load. What is the terminal voltage of the two batteries? You are designing a flashlight, and there are two options to consider. In the first, the flashlight uses one D-cell (sigma = 1.5 V, E = 20.83 W middot hr) to supply a bulb (R = 2.5 ohm, P = 0.9 W). In the second, the flashlight uses two D-cells to supply a bulb (R = 10 ohm, P = 0.9 W). (a) Determine the current drawn from the battery (s) in each of the cases. (b) Considering the lifetime of the battery (s) in each case, which is the better option?

Explanation / Answer

8(a).Emf of real battery E = 1.5 volt

Internal resistance r = 0.5 ohm

Load resistance R = 2 ohm

We know E = i ( R + r )

From this current i = E /(R + r )

= 1.5 /(2+0.5)

= 1.5 / 2.5

= 3/5 = 0.6 A

Terminal voltage of the battery V = iR

= (0.6)(2)

= 1.2 volt

(b).Resultant emf E ' = E + E = 1.5 volt + 1.5 volt = 3 volt

We know E ' = i ' (R + r )

From this current i ' = E ' /( R + r+r )

= 3 /(2+0.5+0.5)

= 3/3

= 1 A

Terminal voltage V ' = i ' R

= (1)(2)

= 2 volt

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