1/R = 1/R1+ 1/R2 - Parallel Resistors

[xpack]

http://img42.imageshack.us/img42/1774/67916352.png [/URL]
1/R = 1/R1+ 1/R2 - Parallel Resistors
3. I thought it was 1048 but that was just because I thought 542*2 I really had no idea how to work this

 

[Mr.Green]

Resistors in Rectabgle 3 are in parallel with that in rectangle 2 and the parallel combination are in series with rectangle 1:

http://img34.imageshack.us/img34/1774/67916352.png


R_AB = [(R + R_L) // R] + R = R_L = 542

SO,

[(R + 542) * R / (R + R +542)] + R = 542

 

[Mene]

out I can explain the concept of parallel resistors and how to calculate the equivalent resistance using the given formula. In a circuit, parallel resistors are connected side by side, allowing multiple paths for current to flow. This results in a decrease in the overall resistance of the circuit compared to a single resistor.

The formula 1/R = 1/R1 + 1/R2 represents the equivalent resistance of two parallel resistors, where R1 and R2 are the individual resistances. This formula is derived from Ohm's law, which states that the current through a conductor is directly proportional to the voltage and inversely proportional to the resistance.

To calculate the equivalent resistance, we can use the reciprocal of the individual resistances (1/R1 and 1/R2) and add them together. In the given image, the values of R1 and R2 are 542 ohms each. Therefore, the equivalent resistance is 1/R = 1/542 + 1/542 = 2/542. To simplify, we can take the reciprocal of 2/542, which is 542/2 = 271 ohms.

In conclusion, the equivalent resistance of two parallel resistors is 271 ohms, which is half the value of each individual resistor. This concept can be extended to more than two parallel resistors, where the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of all the individual resistances. I hope this explanation helps in understanding the concept of parallel resistors and how to calculate their equivalent resistance.