Question

s.
In the given circuit, the effective resistance between points A and C will be


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Answer 1

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Answer 2

Answer:

The effective resistance between points A and C is ⅔R .

Explanation:

• If n number of resistance are connected end to end so that same current flows through each one of them then, they are said to be in series combination.
• The equivalent resistance in series combination is

$R(eq) = R1+ R2 + R3 + ... + Rn$

• If n number of resistances are connected in between two common points so that each of them provide a separate path for current, then then they are said to be in parallel combination.
• The equivalent resistance in parallel combination is

$\frac{1}{R(eq)} = \frac{1}{R1} + \frac{1}{R2} + ... \frac{1}{Rn}$

In given circuit:

• Resistances between path ADC are connected in series.
• Resistances between path ABC are connected in series.
• Resistance ADC, ABC and AC are connected in parallel.
• Resistance between path ADC is given by

$R(ADC) = R + R = 2R$

• Resistance between path ABC is given by

$R(ABC) = R + R = 2R$

• Resistance between path AC is 2R.
• Now, equivalent resistance between point A and C is given by parallel combination of all the three path resistances.

$\frac{1}{R(eq)} = \frac{1}{2R} + \frac{1}{2R} + \frac{1}{2R} \\\frac{1}{R(eq)} = \frac{3}{2R} \\ R(eq)= \frac{2}{3} R$

• Hence, equivalent resistance between points A and C is ⅔R .