When a 3 ohm resistance coil is connected across the terminals of a battery, the current is 1.5 A. When a 5 ohm resistance is connected across the same battery, the current is 1 A. Find the internal resistance of the cell.

Asked by kumar.ashlesha | 16th Jun, 2015, 11:24: AM

Expert Answer:

begin mathsize 12px style The space current space in space circuit space is space given space as comma straight I equals fraction numerator straight E over denominator straight R plus straight r end fraction straight E space is space the space emf space of space the space cell comma space straight R space is space external space resistance space and space straight r space is space the space internal space resistance When space straight a space 3 space ohm space resistance space coil space is space connected space across space the space terminals space of space straight a space battery comma space the space current space is space 1.5 space straight A Hence comma 1.5 equals fraction numerator straight E over denominator 3 plus straight r end fraction rightwards double arrow straight E equals 1.5 open parentheses 3 plus straight r close parentheses space space space space space space space space space left parenthesis straight i right parenthesis similarly comma space When space straight a space 5 space ohm space resistance space is space connected space across space the space same space battery comma space the space current space is space 1 space straight A. 1 equals fraction numerator straight E over denominator 5 plus straight r end fraction rightwards double arrow straight E equals 1 left parenthesis 5 plus straight r right parenthesis space space space space space space space space left parenthesis ii right parenthesis Since space straight E space is space same space for space both space external space resistance comma space comparing space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis space 1.5 open parentheses 3 plus straight r close parentheses space space space equals 1 left parenthesis 5 plus straight r right parenthesis space space 4.5 plus 1.5 straight r equals 5 plus straight r 0.5 straight r equals 0.5 straight r equals 1 space straight capital omega Hence comma space internal space resistance space of space the space cell space is space 1 space straight capital omega end style

Answered by Priyanka Kumbhar | 16th Jun, 2015, 04:31: PM