The total resistance of two circuits in parallel is 15 ohms and one circuit has five times the resistance of the other, find the resistance of each circuit. Use 1/R=1/R1+1/R2. R1 and R2 are two individual resistances.
a)Find the smaller resistance
b)Find the larger resistance
To find the resistance of each circuit, let's use the given formula 1/R = 1/R1 + 1/R2, where R is the total resistance, R1 is the resistance of the first circuit, and R2 is the resistance of the second circuit.
a) Find the smaller resistance:
Let's assume the resistance of the smaller circuit as x ohms. Therefore, the resistance of the larger circuit would be 5x ohms, as it is five times the resistance of the smaller circuit.
Now, we can substitute these values into the formula:
1/R = 1/R1 + 1/R2
1/15 = 1/x + 1/5x
To simplify the equation, we can multiply through by 15x to get rid of the denominators:
15x * (1/15) = 15x * (1/x) + 15x * (1/5x)
1 = 15/x + 3
Next, let's isolate the variable x:
1 - 3 = 15/x
-2 = 15/x
To solve for x, we can cross-multiply:
-2x = 15
Dividing both sides by -2 gives us:
x = -15/2
As resistance cannot be negative, we discard this solution. Therefore, there is no valid smaller resistance.
b) Find the larger resistance:
Since we couldn't find a valid smaller resistance, it means there is no smaller circuit and only one circuit is present. Thus, there is no valid larger resistance.
In conclusion, the given problem seems to have an error or inconsistency. There is no valid solution for the resistance of each circuit based on the given information.
The total resistance of two circuits in parallel is 18 ohms and one circuit has five times the resistance of the other, find the resistance of each circuit. Use 1/R=1/R1+1/R2. R1 and R2 are two individual resistances.
a)Find the smaller resistance
b)Find the larger resistance