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Suppose there is a circull consisting of only resistances and batteries. Suppose one is to double (or increase it to n-times) all voltages and all resistances. Show that currents are unaltered. |
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Answer» Solution :LET equivalent internal resistance of GIVEN cells be `R_(eq). ` Equivalent voltage be `V_(eq)` EXTERNAL resistance be R. From Ohm.s law, `I_(1) = (V_(eq))/(R_(eq) + R) "" `.... (1) When value of resistors and all batteries MADE n times initial value then, `therefore V_(eq) = nV_(eq), R_(eq) = nR_(eq)` and new external resistor R= NR Current in new (modified ) circuit, `I_(1) = (n V_(eq))/(nR_(eq) + nR) = (n V_(eq))/(n (R_(eq) + R)) ` ` = (V_(eq))/(R_(eq)+ R)` `therefore ` Comparing (1) and (2) `I_(1) = I_(1)` thus current do not change. |
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