Question

Two 30k ohm resistors are connected in parallel. The total resistance is ____ kohms.

a. 15k
b. 60k
c. 30k
d. 900k

Answer 1

a. 15 kΩ

Step-by-step explanation:

R1 = 30 kΩ

R2 = 30kΩ

Rtotal = ?

For parallel circuits: 1/R1 + 1/R2 = 1/Rtotal

Solve for Rtotal

1/30 + 1/30 = 1/Rtotal

2/30 = 1/Rtotal

2(Rtotal) = 30

Rtotal = 30/2 = 15 kΩ

Answer 2

Two 30k ohm resistors connected in parallel result in a total resistance of 15k ohms, as calculated using the formula for parallel resistances.

Step-by-step explanation:

When two resistors are connected in parallel, the total resistance is found by using the formula for parallel resistances, which is 1/Rtotal = 1/R1 + 1/R2. So, for two 30k ohm resistors connected in parallel, we calculate the total resistance as follows:

1/Rtotal = 1/30k + 1/30k

1/Rtotal = 2/30k

Now, take the reciprocal of both sides to solve for Rtotal:

Rtotal = 30k/2

Rtotal = 15k

Therefore, the total resistance for two 30k ohm resistors in parallel is 15k ohms (option a). This formula proves vital in determining the overall resistance when multiple resistors are configured in parallel, showcasing how their combined resistance deviates from individual resistances in such arrangements.