Question

Find the total conductance and resistance of four
parallel resistors having ressistances of 1, 0.5, 0.25
and 0.125 ohm? ​

Answer 1

Answer:

total resistance =1.875/0.125

Step-by-step explanation:

R= 1+1/0.5+1/0.25+1/0.125

Answer 2

The total conductance (G) of parallel registers is 15 mho and total resistance(R) is 0.067 ohm.

Given:

• Four parallel resistors.
• 1 ohm, 0.5ohm, 0.25 ohm and 0.125 ohm

To find:

• Find the total conductance and resistance of the circuit.

Solution:

Conductance of parallel combinations of resistors:

Conductance of parallel combination of resisters is addition of individual conductance.

$\bf G = \frac{1}{R_1} + \frac{1}{R_2} +\frac{1}{R_3} + ... + \frac{1}{R_n} \: \: \mho$

Resistance of parallel combinations of resistors:

$\bf R = \frac{1}{G}$

Step 1:

Find the conductance of the circuit.

$G = \frac{1}{1} + \frac{1}{0.5} +\frac{1}{0.25} + \frac{1}{0.125}$

$G = \frac{1}{1} + \frac{10}{5} +\frac{100}{25} + \frac{1000}{125}$

$G =1 + 2+4 +8$

$\bf G = 15 \: \mho$

Thus,

Conductance of circuit is 15 'mho'.

Step 2:

Find the total resistance of the circuit.

As we know that resistance is reciprocal of conductance or vice versa.

So,

$R = \frac{1}{15} \: ohm$

$\bf R = 0.067 \: \: ohm$

Thus,

The equivalent resistance of the circuit is 0.067 ohm.

Thus,

The conductance of circuit is 15 mho and resistance is 0.067 ohm.

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