Question

we have four resistor a b c and d of resistance 4 ohm 8 ohm 12 ohm and 24 ohm respectively calculate: A) lowest resistance which can be obtained by combining this for resistors .B) highest resistance which can be obtained by combining this for resistors

Answer 1

Dear Student,
The lowest resistance that can be obtained by combining four coils ofresistors of 4Ω, 8Ω, 12Ω, 24Ω is 2Ω;

This will be obtained when the coils are connected in parallel combination;

So,

Equivalent resistance in parallel combination is,

1 / Req = 1 / R1 + 1 / R2 + 1 / R3 + 1 / R4

1 / Req = 1 / 4 + 1 / 8 + 1 / 12 + 1 / 24

1 / Req = 6 / 24 + 3 / 24 + 2 / 24 = 1 / 24

1 / Req = 12 / 24

1 / Req = 1 / 2

Req = 2Ω

Now as we see in parallel combination the Equivalent resistance is 2Ω,

Now let us check the Equivalent resistance in series combination:

Rs = R1 + R2 + R3 + R4

Rs = 4 + 8 + 12 +24

Rs = 48Ω

So we see that the Equivalent resistance is less in parallel combination...............

the ratio of maximum to minimum resistance is = 48/2 = 24

Regards