To calculate the total current in a parallel circuit, we first need to determine the total (or equivalent) resistance of the circuit and then apply Ohm's Law.

Step 1: Calculate the total resistance in the parallel circuit

The formula for the total resistance $R_{total}$ in a parallel circuit is:

$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$

Substitute the given values:

$\frac{1}{R_{total}} = \frac{1}{100} + \frac{1}{400} + \frac{1}{200}$

Now, calculate the fractions:

$\frac{1}{R_{total}} = 0.01 + 0.0025 + 0.005$

$\frac{1}{R_{total}} = 0.0175$

Now, take the reciprocal to find the total resistance:

$R_{total} = \frac{1}{0.0175} = 57.14 \, \Omega$

Step 2: Calculate the total current using Ohm's Law

Ohm's Law is:

$I = \frac{V}{R}$

Where:

• $V$ is the voltage (120 V),
• $R$ is the total resistance (57.14 Ω).

Substitute the values:

$I = \frac{120}{57.14} \approx 2.10 \, \text{A}$

Final Answer:

The total current that flows through the circuit is approximately 2.10 A.

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Would you like a more detailed explanation of the steps, or do you have any questions on how this was calculated?

Here are 5 related questions to explore:

1. How would the total current change if one of the resistors in the parallel circuit was removed?
2. How can you calculate the individual current through each resistor in a parallel circuit?
3. What happens to the total resistance in a parallel circuit when more resistors are added?
4. How would the total current change if the power source was changed to 240 V?
5. What is the difference between calculating total current in parallel versus series circuits?

Tip: When calculating total resistance in parallel circuits, the reciprocal formula is key. Always double-check each fraction before summing them up to avoid mistakes!