Electrical Engineering: Basic Laws (15 of 31) Conductance in a Parallel Circuit

Summary

The video explains how to calculate current in parallel circuits using conductance, which is the inverse of resistance. Two resistors (12 ohms and 4 ohms) are analyzed, and their conductances are calculated. The key advantage of using conductance is that it simplifies current calculations, as current in each branch equals the conductance multiplied by the voltage. This approach is contrasted with the traditional method using resistance, showing how both yield the same total current. The video demonstrates that using conductance can make solving parallel circuits faster and easier.

Takeaways

• ⚡ Conductance is the inverse of resistance, and it is easier to use in certain circuit calculations.
• 🔌 In a parallel circuit, the voltage across each branch is always the same.
• 🧮 The conductance in each branch (G) is calculated as 1 over the resistance (R).
• 📐 Using Ohm's Law, current (I) is equal to conductance (G) multiplied by voltage (V).
• 🔄 For branch 1, G1 = 1 / 12 ohms, and for branch 2, G2 = 1 / 4 ohms.
• 💡 The current in the first branch is G1 times the voltage (20V), resulting in approximately 1.67 amps.
• ⚙️ The current in the second branch is G2 times the voltage (20V), giving 5 amps.
• 🔗 The total resistance in the parallel circuit is found using the product-over-sum formula: R_total = (R1 * R2) / (R1 + R2).
• 📊 The total resistance of the circuit is 3 ohms, and the total current is 6.67 amps.
• ✅ Using conductance simplifies finding the current in each branch compared to traditional resistance methods.

Q & A

What is conductance in relation to resistance?

Conductance is the inverse of resistance. It is a measure of how easily electricity flows through a component, and its unit is Siemens (S).

How is the current in a parallel circuit calculated using conductance?

The current in a parallel circuit is calculated by multiplying the conductance of each branch by the voltage across the branch. This is a simplified version of Ohm's law when using conductance.

What is the voltage across each branch in a parallel circuit?

In a parallel circuit, the voltage across each branch is the same. In this example, it is 20 volts across both branches.

How do you calculate the conductance of a resistor?

The conductance (G) of a resistor is calculated as the inverse of its resistance (R). For example, G1 = 1/R1.

What are the conductances of the two resistors in the example?

For the first resistor, G1 = 1/12 Siemens, and for the second resistor, G2 = 1/4 Siemens.

How do you calculate the current in each branch using conductance?

To calculate the current, multiply the conductance by the voltage. For the first branch, I1 = G1 * V, and for the second branch, I2 = G2 * V.

What is the total resistance in the parallel circuit example?

The total resistance is calculated using the product-over-sum formula: R_total = (R1 * R2) / (R1 + R2), which in this case equals 3 ohms.

How is the total current in the circuit determined using resistance?

The total current is found using Ohm's law, I = V / R. With a total voltage of 20 volts and a total resistance of 3 ohms, the current is 6.67 amps.

Does the sum of the branch currents match the total current of the circuit?

Yes, the sum of the branch currents (1.67 amps and 5 amps) equals the total current of 6.67 amps, confirming the calculations are correct.

Why is using conductance easier in parallel circuits compared to using resistance?

Using conductance simplifies the calculation of current in each branch because you only need to multiply the conductance by the voltage, avoiding more complex equations required with resistance.