Current Electricity 3 Question 3

3. A cell of internal resistance r drives current through an external resistance R. The power delivered by the cell to the external resistance will be maximum when

(8 April 2019, II)

(a) R=2r

(b) R=r

(c) R=0.001r

(d) R=1000r

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Solution:

  1. Given circuit is shown in the figure below

Net current, I=ER+r

Power across R is given as

P=I2R=ER+r2R [using Eq. (i 

For the maximum power,

dPdR=0dPdR=ddRE2R+rR=E2ddRR(R+r)2=E2(R+r)2×12R×(R+r)(R+r)4=0(R+r)2=2R(R+r) or R+r=2Rr=R

The power delivered by the cell to the external resistance is maximum when R=r.

Alternate Solution

From maximum power theorem, power dissipated will be maximum when internal resistance of source will be equals to external load resistance, i.e.

r=R.



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