Electricity And Magnitism, Resistance
Electricity and Magnetism
Level
1
The net resistance of two resistors in parallel combination is 2Ω and in series combination is 9Ω. The two resistors are
6Ω , 3Ω
6Ω , 9Ω
2Ω , 6Ω
6Ω , 2Ω
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1 solution
Resistors in Parallel be equation (1): R 1 + R 2 R 1 R 2 = 2 ( 1 ) Resistors in Series be equation (2): R 1 + R 2 = 9 ( 2 ) Plug-in (2) to (1) yields 9 R 1 R 2 = 2 R 1 R 2 = 1 8 ( 3 ) From (2)... R 2 = 9 − R 1 , plug-in at (3) will yield R 1 ( 9 − R 1 ) = 1 8 9 R 1 − R 1 2 = 1 8 Re-arranging terms and equate to zero to solve R 1 , R 1 2 − 9 R 1 + 1 8 = 0 By Factoring, we have ( R 1 − 3 ) ( R 1 − 6 ) = 0 therefore if R 1 = 3 Ω , R 2 = 6 Ω and
if R 1 = 6 Ω , R 2 = 3 Ω .