Current Electricity and Electrical InstrumentHard
Question
For ensuring dissipation of same energy in all three resistors (R1, R2, R3) connected as shown in figure their values must be related as
Options
A.R1 = R2 = R3
B.R2 = R3 and R1 = 4R2
C.R2 = R3 and R1 = (1/4)R2
D.R1 = R2 + R3
Solution
Let i1, i2 and i3 be current in R1, R2and R3.Now, power consumed are same so,
i12R1 = i22R2 = i32R3 ...... (i)
i2R2 = i3R3 [volt over them are same] ...... (ii)
Diving (i)with(ii) i2 = i3 ⇒ R2 = R3 i1 = 2i2 [i1 is equally being divided]
i12R1 = i22R2 =
R2
R2 = 4R1
i12R1 = i22R2 = i32R3 ...... (i)
i2R2 = i3R3 [volt over them are same] ...... (ii)
Diving (i)with(ii) i2 = i3 ⇒ R2 = R3 i1 = 2i2 [i1 is equally being divided]
i12R1 = i22R2 =
R2R2 = 4R1
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