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Q.
What will be the equivalent resistance between the two points $A$ and $D$?
AIPMTAIPMT 1996Current Electricity
Solution:
Lower resistance on extreme left and upper resistance on extreme right are ineffective.
The resistance $R_{2}$ and $R_{3}$ are in series combination.
Therefore their equivalent resistance, $R^{\prime}=R_{2}+R_{3}=10+10=20 \Omega$.
Similarly, the resistance $R_{5}$ and $R_{6}$ are in series combination.
Therefore their equivalent resistance, $R ^{\prime \prime}=R_{5}+R_{6}=10+10=20 \Omega$.
Now the equivalent resistances $R ^{\prime}$ and $R ^{\prime \prime}$ are in parallel combination.
Therefore their equivalent resistance.
$ R^{\prime \prime \prime}=\frac{R^{\prime} R^{\prime \prime}}{R^{\prime}+R^{\prime \prime}}=\frac{20 \times 20}{20+20}=\frac{400}{40}=10 \Omega$.
Thus equivalent resistance between $A$ and $D , R =R_{1}+R^{\prime \prime \prime}+R_{4}=10+10+10=30 \Omega(\because$
series combination)
