Question

Judge the equivalent resistance when Die following are connected in parallel— (a) 1 Ω , 106 Ω , (b) 1 Ω , 103 Ω and 106 Ω.

Answer 1

(a)  1 ohm and 106 times ohm                   R1 = 1 ohm                   R2 = 106 times = 1000000 ohm           Total resistance in parallel 1/R = 1/R1 + 1/R2                   = 1/1 + 1/1000000                   = 1000000+1/1000000                   = 1000001/1000000                   = 1/R = 1/1 ohm (approx)                   Resistance = 1 ohm (approx)

          (b)  R1 = 1 ohm           R2 = 103 ohm           R3 = 106 ohm           Total resistance in parallel

Answer 2

Answer:

Part 'a':

R = 0.99 ohms

Part 'b':

R = 0.914 ohms

Explanation:

For parallel combination, equivalent can be calculated by:

1/R = 1/R1 + 1/R2 + 1/R3 + ...

Where,

'R' is the equivalent or net resistance,

'R1' is the resistance of first resistor,

'R2' is the resistance of second resistor,

'R3' is the resistance of third resistor,

And so on,

Now to compute and compare the equivalent resistance in each case:

Part 'a':

We are given:

R1 = 1ohm

R2 = 106ohms

Thus, for equivalent resistance:

1/R = 1/R1 + 1/R2

1/R = 1/1 + 1/106

Thus;

1/R = 1+1/106

1/R = (106+1)/106

Or, reciprocating the equation;

R = 106/107

Or,

R = 0.99 ohms.

Part 'b':

In this case,

R1 = 1 ohm

R2 = 103 ohm

R3 = 106 ohm

Now, again, for equivalent resistance;

1/R = 1/R1 + 1/R2 + 1/R3

1/R = 1/1 + 1/103 + 1/106

1/R = 1.109

Or,

R = 0.914 ohms

Thus, resistance in part 'b' is lesser as compared to the resistance in part 'a', as for parallel combination, greater resistances reduces the final resistances.