A resistor of length L is connected to a battery and current I is give...
Current through divided resistors
Given
- Length of the resistor = L
- Current through the resistor = I
- The resistor is divided into three parts by lenses, all having the same cross-sectional area
- All parts are connected in parallel with the same battery
Solution
Calculating resistance of the original resistor
The resistance of the original resistor can be calculated using the formula:
R = ρL / A
Where:
- R is the resistance
- ρ is the resistivity of the material
- L is the length of the resistor
- A is the cross-sectional area of the resistor
Calculating resistance of each divided resistor
Since all three parts have the same cross-sectional area, their resistance can be calculated using the formula:
R' = ρ(L/3) / A = ρL / 3A
Calculating total resistance
The total resistance of the divided resistors connected in parallel can be calculated using the formula:
1/Rt = 1/R' + 1/R' + 1/R' = 3/R'
Therefore:
Rt = R' / 3 = ρL / 9A
Calculating current through each divided resistor
Using Ohm's law, we can calculate the current through each divided resistor:
I' = V / R' = VI / ρL / 3A = 3VI / ρL / 9A = 3I
Conclusion
The current through each divided resistor is 3I.