# Two resistors and total resistance

• bkl4life
In summary: Yes. Once you have solved for the resistances, you will be able to calculate the current(s) using Ohm's Law.In a series the equation is just: R1+R2+R3 and for a parallel it is 1/R1+ 1/R2Parallel is 1 / [ (1/R1) + (1/R2) ]"The reciprocal of the sum of the reciprocals."Another form that you can use when there are exactly two resistors is R1 R2 / (R1 + R2)"The product over the sum."
bkl4life

## Homework Statement

Two resistors, R1 and R2, have an equivalent resistance of 710 ohms when they are connected in series and an equivalent resistance of 200 ohms when they are connected in parallel.

a) what are R1 and R2
b) Determine the current traveling through the resistors when they are connected in series and parallel to a 12 v battery.

V=IR

## The Attempt at a Solution

R1 and R2 are different.

In a series the equation is just: R1+R2+R3 and for a parallel it is 1/R1+ 1/R2

R1 and R2 must add up to get 910 (total).

I'm just not sure how.

I am a little confused by the wording. What do you mean by "equivalent resistance"? Do you mean the total resistance or that they are equivalent (the same)? If it is the former, then why must they add up to 910 ohm? Don't they add up to 710 when connected in serial?

Equivalent resistance here means total... I think. The question seems easy and yet I can't do it.

I think the wording may be confusing you. This may help clear it up:

The total resistance when the 2 resistors are connected in series is 710 ohms.
The total resistance when the 2 resistors are connected in parallel is 200 ohms.

With this information, how many independent equations can you write? How many unknowns do you have?

Once you have solved for the resistances, you will be able to calculate the current(s) using Ohm's Law.

bkl4life said:
In a series the equation is just: R1+R2+R3 and for a parallel it is 1/R1+ 1/R2

Parallel is 1 / [ (1/R1) + (1/R2) ]

"The reciprocal of the sum of the reciprocals."

Another form that you can use when there are exactly two resistors is R1 R2 / (R1 + R2)

"The product over the sum."

I have never done a problem like this. In class we are given the total resistance or a drawing. I'm not sure what to do when I am given the total resistance and have to find the two resistors.

For parallel: 150=1/r1+1/r2

Would I get the same answer for the two resistors.
To solve for 1/r1 I could plug 1 in for r2 and I end up getting::

R1=1/149= .00667

You have two unknown, R1 and R2, and you have two equations, one for the connection in series and one for the connection in parallel. With two unknowns and two equations, you can simply set up your system of equations and solve for R1 and R2.

Can you write the two equations?

## What is the formula for calculating total resistance in a circuit with two resistors?

The formula for calculating total resistance in a circuit with two resistors is Rtotal = R1 + R2, where R1 and R2 are the individual resistances of the two resistors.

## How do resistors in a series circuit affect the total resistance?

In a series circuit, the resistors add up to create a greater total resistance. This is because the current has to pass through each resistor, resulting in a greater overall resistance.

## What happens to the total resistance if the two resistors in a parallel circuit are equal?

If the two resistors in a parallel circuit are equal, the total resistance will be half of the resistance of each individual resistor. This is because in a parallel circuit, the current is divided between the two resistors, resulting in a lower overall resistance.

## Can the total resistance in a circuit ever be lower than the resistance of the smallest resistor?

No, the total resistance in a circuit can never be lower than the resistance of the smallest resistor. This is because the total resistance is determined by the sum of all the resistors in the circuit, and the smallest resistor will always contribute to the overall resistance.

## How can I calculate the total resistance in a circuit with more than two resistors?

To calculate the total resistance in a circuit with more than two resistors, you can use the formula Rtotal = R1 + R2 + R3 + ... + Rn, where Rn is the resistance of each individual resistor in the circuit. Simply add up the resistances of all the resistors to get the total resistance.

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