Calculate Unknown Resistance in Parallel Circuit

[Bryster77]

a 3.3ohm resistor and another resistor are connected in parallel across a 3v battery. the current in the circuit is 1.41 A. Find the uknown resistance

R=(1/3.3 + 1/x)^-1

V=IR
3v= 1.41A(R)
R= 2.13 ohm

this is where i got stuck...

2.13 ohm= (1/3.3 ohm + 1/x ohm)^-1

how do i go about finding x...

the answer is 6 ohm but I am curious how. :D ty

 

[Bryster77]

nevermind i got it

 

[nlightner]

To find the unknown resistance, we can use the equation for calculating the equivalent resistance in a parallel circuit:

1/R_eq = 1/R1 + 1/R2 + 1/R3 + ...

In this case, we have two resistors in parallel, so we can rewrite the equation as:

1/R_eq = 1/3.3 ohm + 1/x ohm

We can substitute the known values for the 3.3 ohm resistor and the current, and solve for x:

1/R_eq = 1/3.3 ohm + 1/x ohm
1/R_eq = 0.303 ohm^-1 + 1/x ohm
1/R_eq = (0.303 + 1/x) ohm^-1
R_eq = (1/(0.303 + 1/x)) ohm

Now, we know that the equivalent resistance in a parallel circuit is equal to the voltage divided by the current, so we can set this equal to 3v/1.41A and solve for x:

R_eq = (1/(0.303 + 1/x)) ohm
3v/1.41A = (1/(0.303 + 1/x)) ohm
2.13 ohm = (1/(0.303 + 1/x)) ohm
2.13 ohm * (0.303 + 1/x) = (1/x) ohm
0.646 + 2.13/x = 1/x ohm
0.646 = (1/x - 2.13/x) ohm
0.646 = (-1.13/x) ohm
x = -1.13/0.646 ohm
x = -1.75 ohm

However, a negative resistance does not make sense in this context, so we can conclude that there must have been an error in the calculations.

To find the correct value of x, we can use the formula for calculating the current in a parallel circuit:

I_total = I1 + I2 + I3 + ...

In this case, we only have two resistors, so we can rewrite the equation as:

I_total = I1 + I2
I_total = V/R1 + V/R2
I_total = V (1/R1 + 1/R2)
1.41A