Question

A 100 Ohm, 200 Ohm, and 400 Ohm resistors are in parallel with each other. What is the equivalent

resistance? Which resistor would draw the most current, and why?

Answer 1

1/R = 1/R1 + 1/R2 + 1/R3

1/1 + 1/2 + 1/4 = 1 + .5 + .25 = 1.75

1/1.75 = .572

multiplying this by 100 gives us

R = 57.2 ohms

The smallest resistor (100 ohms) will draw the most current

(One can also use R = R1 R2 R3 / (R1 R2 + R1 R3 + R2 R3)

Answer 2

Hi there!

We can use the following equation to solve for equivalent resistance:

`(1)/(R_T) = (1)/(R_1) + (1)/(R_2) + ... + (1)/(R_n)`

We can plug in the givens and solve.

`(1)/(R_T) = (1)/(100) + (1)/(200) + (1)/(400) \\\\(1)/(R_T) = 0.175\\\\R_T = (1)/(0.175) = \boxed{57.143 \Omega}`

The resistor that would draw the most current is the 100 Ohm resistor because current chooses the path of LEAST RESISTANCE. This can also be proved mathematically with the following:

For resistors in parallel, the POTENTIAL DIFFERENCE (VOLTAGE) is the same.

Since I = V/R, a smaller 'R' means a larger 'I'. Thus, the smallest resistor would have the greatest current through it.