A diagram of a closed circuit with a power source on the left labeled 6 V. There are 3 resistors in parallel, separate paths, connected to it labeled B 10 Ohms, C 20 Ohms and D 50 Ohms. The branch with the power source is labeled A. There are vectors in the clockwise direction across all three resistors and in the branch with the power source. Perform calculations using the circuit illustrated. Round all the numerical answers to the tenths place. The total resistance in the circuit is Ω. The expected current at point A is A. At what point in the circuit will the current be the lowest (A, B, C, or D)?

To calculate the total resistance in the circuit with resistors in parallel, you use the formula for total parallel resistance:

1 / R_total = 1 / R1 + 1 / R2 + 1 / R3

Where R1, R2, and R3 are the resistances of the individual resistors in parallel. Plugging the values from the problem:

1 / R_total = 1 / 10 + 1 / 20 + 1 / 50 1 / R_total = 0.1 + 0.05 + 0.02 1 / R_total = 0.17

Now, take the reciprocal to find R_total:

R_total = 1 / 0.17 R_total ≈ 5.9 Ω (rounded to the tenths place)

Next, to find the expected current at point A (I_A), we use Ohm's law:

V = I * R

Where V is the voltage across the power source (6 V), I is the current, and R is the resistance. Rearranging the formula to solve for I gives us:

I = V / R

Substituting the total resistance and the voltage into the formula:

I_A = 6 V / 5.9 Ω I_A ≈ 1.02 A (rounded to the tenths place)

As for the point in the circuit where the current will be the lowest: In a parallel circuit, the current divides among the paths with inverse proportionality to the resistance of each path (lesser current through higher resistances). Therefore, the branch with the highest resistance will have the lowest current. In this case:

Branch B (10 Ohms) - Moderate current Branch C (20 Ohms) - Lower current Branch D (50 Ohms) - Lowest current

Hence, the point in the circuit where the current will be the lowest is at point D.

Extra: In a parallel circuit, the voltage across each resistor is the same as the voltage of the power source. This means that each resistor in the illustration (B, C, D) has the same 6 V across it. The total resistance in a parallel circuit is always less than the smallest individual resistance in the circuit because adding additional pathways for the current to travel through lowers the overall resistance.

Ohm's Law is a fundamental principle in electronics and physics that relates voltage (V), current (I), and resistance (R). This law states that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them.

For understanding parallel circuits, it's crucial to remember these two points:

1. The voltage is the same across all components in a parallel circuit. 2. The total current in the circuit is the sum of the currents through each component.

The reason the total resistance in a parallel circuit is less than the smallest resistor is that each additional resistor provides a new pathway for the current to travel, effectively increasing the total "conducting area" available for the current, thus reducing the overall resistance. When you understand the flow of electricity in terms of pathways, it's similar to adding more lanes to a highway; more lanes mean less resistance to the flow of traffic, just as more pathways mean less electrical resistance.