The resistance across M and N in the given fi | vedclass

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Question

(B) The circuit consists of a delta configuration connected to points $B$ and $C$. The resistors are arranged such that there is a resistor $r$ betwee

Vedclass · Accepted Answer

$r/3$

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(B) The circuit consists of a delta configuration connected to points $B$ and $C$. The resistors are arranged such that there is a resistor $r$ between $B$ and $C$,and two branches from $A$ to $B$ and $A$ to $C$ each having resistors. Specifically,the circuit can be simplified by recognizing that the resistors connected to node $A$ form a series combination with each other,which is then in parallel with the resistor directly between $B$ and $C$. $1$. The two resistors in the upper branches (from $A$ to $B$ and $A$ to $C$) are in series,giving an equivalent resistance of $r + r = 2r$. $2$. This combination of $2r$ is in parallel with the resistor $r$ connected directly between $B$ and $C$. $3$. The equivalent resistance $R_{eq}$ between $M$ and $N$ (which are connected to $B$ and $C$) is given by the parallel formula: $1/R_{eq} = 1/(2r) + 1/r = (1 + 2) / (2r) = 3 / (2r)$. $4$. Therefore,$R_{eq} = 2r/3$.

The resistance across $M$ and $N$ in the given figure is

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