What is the resulting total resistance if two resistors having 5 and 10 ohms resistance are connected in parallel?

Answer 1

3.333 ohms

How do we calculate the answer?

It is calculated from the "Resistors In Parallel Connection Law" which is:

1 / RTOTAL = 1 / R1 + 1 / R2

In this case:

R1 = 5 and R2 = 10

So:

1 / RTOTAL = 1/5 + 1/10 = 0.2 + 0.1 = 0.3

So:

RTOTAL = 1 / 0.3 = 3.333

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For any number of resistors in parallel . . .

Total effective resistance = 1/(1/A + 1/B + 1/C + 1/D + . . . . .)

(If you're working with resistor combinations, then you're supposed to know this formula.)

If there are only two resistors in parallel, and you use the same formula and simplify it,

the total effective resistance turns out to be (A)x(B)/(A + B) .

(Just say to yourself "the product over the sum" and you'll remember it.)

When the two resistors are 5 ohms and 10 ohms, the total effective resistance is:

(5)x(10)/(5+10) = 50/15 = 31/3ohms

Answer 2

The total resistance in parallel can be calculated using the formula: 1/RT = 1/R1 + 1/R2. Substituting the values for R1 and R2 (5 and 10 ohms), we get 1/RT = 1/5 + 1/10. Simplifying, we find RT = 3.33 ohms.