In a parallel circuit, the total or equivalent resistance $R_{total}$ is given by the formula:

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

Where:

• $R_1 = 4.0 \, \Omega$
• $R_2 = 1.0 \, \Omega$
• $R_3 = 2.0 \, \Omega$

Substituting the values into the formula:

$\frac{1}{R_{total}} = \frac{1}{4.0} + \frac{1}{1.0} + \frac{1}{2.0}$

First, calculate each term:

$\frac{1}{4.0} = 0.25, \quad \frac{1}{1.0} = 1.0, \quad \frac{1}{2.0} = 0.5$

Now, add the values:

$\frac{1}{R_{total}} = 0.25 + 1.0 + 0.5 = 1.75$

Finally, take the reciprocal to find $R_{total}$:

$R_{total} = \frac{1}{1.75} \approx 0.571 \, \Omega$

So, the overall resistance of the parallel circuit is approximately 0.571 Ω.

Let me know if you need any further explanation or help!

Related Questions:

1. What happens to the overall resistance in a parallel circuit if more resistors are added?
2. How do you calculate the current in a parallel circuit with a known voltage and total resistance?
3. What is the significance of the formula for parallel resistors?
4. How does the voltage behave across each resistor in a parallel circuit?
5. What is the power dissipation in the circuit given the total resistance and voltage?

Tip:

In parallel circuits, the total resistance always decreases when you add more resistors because each additional path allows more current to flow.