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For three resistors of different value connected in series obtain equation of equivalent resistance. From this write equation of n resistors connected in series. |
Answer» Solution :`R_(1) , R_(2) and R_(3)` are connected with battery of V volt between A and B current in the circuit is I. Potential difference across `R_(1) , R_(2) and R_(3) ` be `V_(1) , V_(2) and V_(3)`. `rArr "" V_(1) = I R_(1), V_(2) = IR_(2) and V_(3) = IR_(3)` `rArr` terminal voltage of battery, `V = V_(1) + V_(2) + V_(3)` `therefore V = IR_(1) + IR_(2) + IR_(3)` `therefore (V)/(I) = R_(1) + R_(2) + R_(3)` `rArr` But `(V)/(I)` is EQUIVALENT resistance ov resistors connected in series. `therefore(V)/(I) = R_(EQ)` `therefore R_(eq) = R_(1) + R_(2) + R_(3)` If n resistance are connected in series then, `R_(eq) = R_(1) + R_(2) + .... +R_(n)` `rArr` If n resistors of EQUAL value R are connected in series then, `R_(eq) = nR` `rArr` In series connection of resistors equivalent resistance is LARGER than largest value. |
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