Find the equivalent resistance of the combination of resistors shown in the figure below.
R1=1.52 microohms
R2= 21.1microohms
no figure. But, you know that if R1 and R2 are in series, then
R = R1 + R2
If they are in parallel, then
1/R = 1/R1 + 1/R2
www.webassign.net/webassignalgphys1/21-p-008.gif
To find the equivalent resistance of the combination of resistors in the figure, you can use the formula for resistors in parallel. Resistors in parallel have the reciprocal of their resistances summed together, which is then inverted.
The formula for resistors in parallel is:
1 / Req = 1 / R1 + 1 / R2
Given:
R1 = 1.52 microohms
R2 = 21.1 microohms
First, convert the resistances to a common unit, such as ohms:
1 microohm = 10^-6 ohms
So, R1 = 1.52 microohms = 1.52 * 10^-6 ohms
And, R2 = 21.1 microohms = 21.1 * 10^-6 ohms
Next, substitute the values into the formula for resistors in parallel:
1 / Req = 1 / (1.52 * 10^-6) + 1 / (21.1 * 10^-6)
Now, simplify the formula:
1 / Req = (1 / 1.52) * 10^6 + (1 / 21.1) * 10^6
Add the fractions:
1 / Req = (10^6 / 1.52) + (10^6 / 21.1)
Calculate the values:
1 / Req = (657894.74) + (47463.41)
1 / Req = 705358.15
Finally, take the reciprocal of both sides to find the equivalent resistance:
Req = 1 / (705358.15)
Using a calculator, you can evaluate this expression to find the equivalent resistance of the combination of resistors.
so plug in your numbers and resolve each branch.
For example, on the right side, the .75 in || with 21.1 = 0.72
So now you have 1.5 in series with 0.72, so that's like a 2.22 resistor there.
Now work through the branch on the left, and you will be left with three resistances in parallel, so just apply the parallel R formula for three values.