A simple parallel circuit is set up with three resistors of values 15 ohms, 35 ohms, and 65 ohms.?

Question

What is the equivalent resistance of the circuit?
1.1 x 10-1ohms
1.9 x 101 ohms
9.0 ohms
1.9 x 102 ohms

Can you help me please :( I have tried and tried

Answer 1

resistors add in parallel using a funny rule

1/Rtotal = 1/R1 + 1/R2 + 1/R3

So take the inverses of all the resistances, add them, and take the inverse of that.

That's your answer.

HINT: Since this is multiple choice, you can tell the answer without doing any math. The answer should be just a bit less than the lowest resistance. Resistors in parallel have less resistance than the individual parts. There's only 1 answer that's even in the ballpark.

Answer 2

It is 9.0 ohms.

Resistances in parallel use the formula:

R(t) = 1 / {1/R(1) + 1/R(2) + 1/R(3) + ...}

That basically says take the reciprocal of each resistance, add all the reciprocals together, then take the reciprocal of that sum. So: R(t) = 1 / {1/15 + 1/35 + 1/65} = 9.04 ohms and in significant digits that comes to 9.0 ohms (can't forget to use only the significant digits!).

If that seems to obnoxious for words and you want another way to do the problem, then do the following. (You know how teachers show you the steps for deriving formulas like the one above? This assumes such an explanation happened but you stopped along the way instead of going all the way to the end!) In a three resistance parallel circuit, you have essentially three separate circuits so pick some handy voltage and calculate the current that flows through each of the three resistors. Let's say we pick 15V. So you have 15V/15ohms = 1 amp, 15V/35ohms = 3/7 amp and 15V/65ohms = 3/13 amps. Now, since we are pretending it's all one load when we pretend it's all one resistance, just add all the currents up: (1 + 3/7 + 3/13) amps = 1.659341 amps. Finally, since resistance = voltage/current, the total resistance, R(t), equals 15V / 1.659341 amps = 9.04 ohms or, in significant digits, 9.0 ohms.

And all you had to do was pick some voltage, any voltage, and use variations of V = I * R.

Answer 3

1/ Rt = 1/R1 + 1/R2 + 1/R3

Rt = total resistance in circuit

1/ Rt = 1/15 + 1/35 + 1/65
= 1/5 x ( 1/3 + 1/7 + 1/13) =
= 1/5 x ( (91 + 39 + 21 )/ (3 x 7 x 13))
= 1/5 x (151 / 273) = 151/1365

so Rt = 1365/151 ohms

which is approximately = 9 ohms

Answer 4

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

So 1/R = 1/15 + 1/35 + 1/65 = 1/(3 X 5) + 1/(7 X 5) + 1/(13 X 5)

which can be written as 1/5 [ 1/3 + 1/7 + 1/13 ] = 1/5 [ (91 + 39 + 21) / 273] = 151 / (5 X 273)

So, R = 5 X 273 / 151 = 9.04 ohms approx.

Answer 5

9 ohms

R(equivalent) =1/ (1/r1 +1/r2 + 1/r3)