Four resistors, each of resistance R and a key K are connected as shown in the figure. The equivalent resistance between points A and B when key K is open will be:
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When dealing with resistors in series and parallel, simplify the circuit step by step. First, combine resistors in series or parallel, then combine the resulting resistances. This method makes the problem easier to solve.
When key $K$ is open, the resistors form a combined series and parallel configuration. Two resistors between points $A$ and $B$ are in parallel. Two additional resistors are in series with this parallel grouping.
1. The parallel resistors between $A$ and $B$ yield an equivalent resistance:
\[R_{\text{eq}} = \frac{R}{2}\]
2. This equivalent resistance is in series with another resistor $R$, resulting in a total equivalent resistance:
\[R_{\text{total}} = R + \frac{R}{2} = \frac{3R}{2}\]
Therefore, the equivalent resistance between points $A$ and $B$ with key $K$ open is \( {\frac{3R}{2}} \).
