Two lamps can be connected to a battery in a circuit in series or in parallel. You can calculate the total resistance RT (t is down from r) in a circuit if you know the resistance in each lamp. Resistance is measured in ohms. For a circuit connected in series, RT = R1 + R2. For a circuit connected in parallel, 1/RT = 1/R1 + 1/R2.
a. The lamps are connected in parallel. RT = 12 ohms. Find R2. R1 is 30 ohms.
Can you show me how to solve 1/12 = 1/30 + 1/r?
a. 1/12=1/x+1/30
30=12*30/X +12
18=360/X
X=20
1/12 = 1/30 + 1/r
The LCD is 60r , so multiply each term by 60 r
60r(1/12) = 60r(1/30) + 60r(1/r)
5r = 2r + 60
3r = 60
r = 20
or
1/12 - 1/30 = 1/r
5/60 - 2/60 = 1/r
3/60 = 1/r
1/20 = 1/r
cross-multiply
r = 20
Thanks to both of you!
To solve the equation 1/12 = 1/30 + 1/R2, we can follow these steps:
Step 1: Simplify the equation by finding a common denominator.
Multiply both sides of the equation by the product of 12, 30, and R2. This step helps eliminate the fractions.
(12 * 30 * R2) * (1/12) = (12 * 30 * R2) * (1/30 + 1/R2)
After simplification, the equation becomes:
30R2 = 12 * R2 + 12 * 30
Step 2: Simplify the equation further.
Distribute on the right side of the equation:
30R2 = 12R2 + 360
Step 3: Move the terms with R2 to the left side of the equation and the constant term to the right side.
Subtract 12R2 from both sides:
30R2 - 12R2 = 360
Simplify the left side of the equation:
18R2 = 360
Step 4: Isolate R2 by dividing both sides of the equation by the coefficient of R2.
Divide both sides by 18:
(18R2)/18 = 360/18
Simplify:
R2 = 20
Therefore, the value of R2 is 20 ohms.