What will be the total resistance and current in a parallel circuit with a 15-volt battery and 3 10-ohm resistors?
Total R.
1/R = 1/R1 + 1/R2 + 1/R3
Then I = E/R
To find the total resistance in a parallel circuit, you need to use the formula:
1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...
In this case, you have three resistors with a value of 10 ohms each. So, the calculation would be:
1/R_total = 1/10 + 1/10 + 1/10
Now, let's calculate the total resistance:
1/R_total = 3/10
To simplify the equation, take the reciprocal of both sides:
R_total = 10/3 ohms
Now, let's calculate the current in the circuit using Ohm's Law:
I = V / R_total
Given that the battery voltage is 15 volts and the total resistance is 10/3 ohms, we can substitute these values into the formula:
I = 15 / (10/3)
To divide by a fraction, multiply by its reciprocal:
I = 15 * (3/10)
I = 45/10
Finally, simplify the fraction:
I = 4.5 amperes
Therefore, the total resistance in the circuit is 10/3 ohms, and the current flowing through the circuit is 4.5 amperes.