Calculating Total Resistance and Current in a Parallel Circuit
How to calculate the total resistance and current in a parallel circuit?
Consider four parallel resistors with equal values of 200 Ohms each connected to a 12V power source. What is the total resistance, RT, and the total current, IT?
Answer:
The total or equivalent resistance, RT, in a parallel circuit can be calculated using the formula 1/RT = 1/R1 + 1/R2 + 1/R3 + 1/R4, where R1, R2, R3, and R4 are the individual resistor values. In this case, since all four resistors have the same value, the formula simplifies to 1/RT = 4/R, where R is the resistance of each individual resistor.
Using this formula, the total resistance, RT, is calculated to be 50 Ohms. Additionally, the total current, IT, in the circuit can be determined using Ohm's Law, I = V/R, where V is the voltage (12V) and R is the total resistance. Substituting the values, the total current, IT, is calculated to be 0.24 Amperes (A).
Explanation:
In the given scenario, four resistors with equal values are connected in parallel to a 12V power source. When resistors are connected in parallel, the total resistance is determined by considering the inverse sum of the reciprocals of each individual resistor's resistance. For our case with equal resistor values, this simplifies to 1/RT = 4/R.
Calculating the total resistance, RT, results in a value of 50 Ohms. To find the total current, IT, Ohm's Law is applied using the total resistance and the voltage source. Substituting the values into the equation, IT is calculated to be 0.24A.
Thus, the correct answers to the question are a) RT = 50 Ohms, and b) IT = 0.24A. By understanding the principles of parallel circuits and applying relevant formulas, the total resistance and current values in such circuits can be accurately determined.