Question
- Calculate the equivalent resistance of the given electrical network between points A and B.
- Also calculate the current through CD and ACB if a 10V dc source is connected between points A and B and the value of $\text{R}=2\Omega.$
✓
Answer
- The equivalent circuit is shown in fig. It is a balanced Wheatstone bridge.
So, the resistance connected between C and D is ineffective.
Resistance of arm ACB, R1 = R + R = 2R
Resistance of arm ADB, R2 = R + R = 2R
Equivalent resistance between A and B, RAB is given by
$\frac{1}{\text{R}_\text{AB}}=\frac{1}{2\text{R}}+\frac{1}{2\text{R}}=\frac{2}{2\text{R}}$
$\Rightarrow\text{R}_\text{AB}=\text{R}=2\Omega$
- In arm CD, there is no current, ICD = 0,
Current through arm ACB
$\text{i}_1=\frac{\text{V}}{\text{R}_1}$
$=\frac{10}{2\text{R}}=\frac{10}{2\times2}=\frac{10}{4}=2.5\text{A}$
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