Three resistors of resistance 2ohms, 3ohms, 2ohms connected in series afterwards parallel. Calculate the effective resistance between p and q
I have no idea what p and q are.
If the three are in series, their resistances add.
R = 2 + 3 + 2 = 7 Ohms
If the three are in parallel, their conductances, 1/R , add
1/R = 1/2 + 1/3 + 1/2 = 3/6 + 2/6 + 3/6 = 8/6 = 4/3
so R = 3/4 Ohm
To calculate the effective resistance between points p and q, we need to first find the total resistance in the series combination of resistors and then calculate the equivalent resistance for the parallel combination.
1. Series Combination:
When resistors are connected in series, the total resistance is simply the sum of the individual resistances.
In this case, the resistors of 2 ohms, 3 ohms, and 2 ohms are connected in series.
So, the total resistance in the series combination is:
R_total = R1 + R2 + R3
= 2 ohms + 3 ohms + 2 ohms
= 7 ohms
2. Parallel Combination:
To find the effective resistance of resistors connected in parallel, we can use the following formula:
1/R_total = 1/R1 + 1/R2 + 1/R3 + ...
In this case, we have only three resistors in parallel.
So, the reciprocal of the total resistance in the parallel combination is:
1/R_total = 1/R1 + 1/R2 + 1/R3
= 1/2 ohms + 1/3 ohms + 1/2 ohms
= 5/6 ohms
Now, to find R_total, we take the reciprocal of the above value:
R_total = 1 / (5/6)
= 6/5 ohms
Therefore, the effective resistance between points p and q is 6/5 ohms or 1.2 ohms.