A piece of wire of resistance, R and uniform cross sectional area, A is cut into four equal parts and bundled together to form a thicker wire. The resistance of the bundled wire is:
A 16R
B 1/4R
C 4R
D 1/16R
It's either 16 or 1/16 im not sureee. So I need help for the working part! Thanks :)
R/4 Ohms/wire.
Rb = 1/4 * R/4 = R/16 or 1/16R = Resistance of the bundle.
As R is inversly propotional to area so resistance will be
R= 1÷A
R= 1/4R
To find the resistance of the bundled wire, we need to consider the concept of resistors in series and in parallel.
When four equal parts of the wire are bundled together, they are essentially connected in parallel. This means that the resistance of the bundled wire will be less than the resistance of the individual wire.
In the case of resistors in parallel, the total resistance (R_total) can be calculated using the formula:
1/R_total = 1/R1 + 1/R2 + 1/R3 + ...
In this case, since all four parts of the wire are of equal resistance (R), we can rewrite the formula as:
1/R_total = 1/R + 1/R + 1/R + 1/R
= 4/R
Now, to find the resistance of the bundled wire (R_total), we can rearrange the equation:
R_total = R/4
Therefore, the resistance of the bundled wire is 1/4 (or 0.25) times the resistance of each individual wire. Therefore, the correct answer is option B: 1/4R.
Hope this helps! Let me know if you have any further questions.