A wire of uniform thickness with a resistance of 27 ohm is cut into three equal pieces and are joint in parallel.find the resistance of the parallel combination.
Correction:
R1 = R2 = R3 = 27/3 = 9 Ohms, each.
When connected in parallel:
Re = 9/3 = 3 Ohms.
given:
A wire of uniform thickness with a resistance =27 ohm
find:
equivalent resistance in parallel
solution:
resistance of each wire=27/3=9
therefore when in parallel equivalent resistance=
1/rp=1/9+1/9+1/9
=3/9=1/3
therefore rp=3 ohm
R = 27Ohm/3 = 9 Ohms.
r =
To find the resistance of the parallel combination, we need to understand the concept of resistors in parallel.
When resistors are connected in parallel, the total resistance (RT) can be calculated using the formula:
1/RT = 1/R1 + 1/R2 + 1/R3 + ...
In this case, since the wire is cut into three equal pieces and joined in parallel, we can assume that each piece has the same resistance. Let's call this resistance R.
So, we can rewrite the formula as:
1/RT = 1/R + 1/R + 1/R
Simplifying further:
1/RT = 3/R
To find the resistance of the parallel combination, we need to isolate RT. We can do this by taking the reciprocal of both sides of the equation:
RT = 1 / (3/R)
Now, we rearrange the equation:
RT = R / 3
Since the resistance of each piece is given as 27 ohm, R = 27 ohm.
Substituting the value of R into the equation:
RT = 27 ohm / 3
RT = 9 ohm
Therefore, the resistance of the parallel combination is 9 ohm.