Electricity, resistance, current, voltage, physics

Question

a circuit operates at 1000 watts, within the circuit we have a 10 ohm, 20 ohm, and 40 ohm resistors.

a) if the resistors are connected in parallel, what would their equivalent resistance be?

b) based on the equivalent resistance, what would the current of the circuit be?

c) what is the voltage required?

Answer 1

Hi Paulina!

a) Equivalent resistance for parallel resistors is given by the equation: 1/Rt = 1/R1 + 1/R2 + 1/R3, where Rt is the total equivalent resistance and R1 through R3 are the resistances of the parallel resistors. Filling in this equation with the value you gave, we get: 1/Rt = 1/(10 ohms) + 1/(20 ohms) + 1/(40 ohms). We can put the right side of the equation into a calculator and get 1/Rt = 7/40. We need to flip both sides of the equation to get: Rt = 40/7 = 5.71 ohms.

b) Ohm's Law tells us that: V = IR where V = voltage, I = current, R = resistance. We want to find current so we rearrange the equation to be I = V/R. We can substitute our values to get: I = (1000 watts)/(5.71 ohms) and divide to get: I = 175.1 amps.

c) This one we are not able to answer unless we know what is required. For example, if the question was instead "What is the voltage required for the current in the circuit to be 200 amps?" then we could solve that problem.