Answer:
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)
Hi there!
We can use the following equation to solve for equivalent resistance:
[tex]\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n}[/tex]
We can plug in the givens and solve.
[tex]\frac{1}{R_T} = \frac{1}{100} + \frac{1}{200} + \frac{1}{400} \\\\\frac{1}{R_T} = 0.175\\\\R_T = \frac{1}{0.175} = \boxed{57.143 \Omega}[/tex]
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.
