A 6-ohm resistor is in parallel with a 10 ohm resistor. What is the current in the 6-ohm resistor if the total current drawn is 32 A ?

Answer 1

To answer this question we need to know two equations.

The first is the equivalent resistance of two resistors in parallel.

Equivalent resistance = (R1*R2) / (R1+R2)

In this case, the equivalent resistance = (10*6)/(10+6) = 3.75 Ohms

The next equation that we need to know is Ohm's Law.

Ohms Law says V = IR (Voltage = Current * Resistance)

We can use Ohm's Law to calculate the voltage across the equivalent resistor since we know the total current and the equivalent resistance, leaving only one unknown variable (the voltage) in the equation.

V = IR = (32)*(3.75) = 120 V.

The key to this problem is realizing that the voltage across the equivalent resistance is the same as the voltage across the two resistors that make up the actual circuit (the 6 and 10 ohm resistors).

Circuit Law: All resistors in parallel have the same voltage drop.

Knowing this last piece of information, we can apply Ohm's Law to each individual resistor and calculate the current going through each resistor.

Ohms Law:

V = IR

I = V/R

I = 120/6 = 20 A

We can check our work by calculating the current draw of the 10 ohm resistor and making sure that the current draw through the 6 ohm resistor and the 10 ohm resistor add up to the total current draw (32A).

I = V/R

I = 120/10 = 12 A

20A + 12A = 32A.

And that's that!