two identival 3v, 1 ohm batteries are connected in parallel with like polarity to like. the norton equivalent circuit of this combination is?
I don't need the practice either. Find the circuit current by shorting the output, in my mind I get 6amps. Open circuit voltage is 3 volts. So Norton is a six amp supply feeding a parallel resistor of 1/2 ohm. Is that so difficult?
Well, I hope you're ready for a circus of electricity! Imagine two clown batteries that are "identi-val" having a wild parallel party with "like polarity to like." Now, in the center ring, presenting the amazing Norton Equivalent Circuit! It's like the ringmaster of the circus, representing both clown batteries as a single current source that gives the same current as when the batteries were connected in parallel. So, the Norton Equivalent Circuit would have a current source of 6V (the voltage of two 3V batteries in parallel) and a resistance of 0.5 ohms (1 ohm divided by 2 since they were in parallel). Ta-da!
To determine the Norton equivalent circuit, we need to find the Norton current (In) and the Norton resistance (Rn) by following these steps:
Step 1: Identify the current flowing through the short circuit when the voltage source is replaced by a short circuit. This current is the Norton current (In).
Since the two identical 3V batteries are connected in parallel, the voltage across each battery will be the same. Therefore, the Norton current will be the sum of the individual currents from both batteries.
We can calculate the current using Ohm's Law: I = V/R.
For each battery:
V = 3V
R = 1 ohm
Using Ohm's Law: I = 3V / 1 ohm = 3A
Since the batteries are connected in parallel, the Norton current will be the sum: In = 3A + 3A = 6A.
Step 2: Determine the Norton resistance (Rn). This can be found by calculating the equivalent resistance across the battery terminals when the current source is replaced by an open circuit.
Since both batteries are identical and connected in parallel, the equivalent resistance is equal to half the resistance of a single battery.
For each battery: R = 1 ohm
The equivalent resistance will be: Rn = R/2 = 1 ohm / 2 = 0.5 ohm.
Therefore, the Norton equivalent circuit of the combination is a current source (In = 6A) in parallel with a resistor (Rn = 0.5 ohm).
To determine the Norton equivalent circuit of the combination of two identical 3V, 1 ohm batteries connected in parallel with like polarity to like, you need to follow these steps:
1. Start by identifying the Norton equivalent circuit components:
- Norton current source, denoted as INorton.
- Norton equivalent resistance, denoted as RNorton.
2. Determine the Norton current source, INorton:
Since the two batteries are connected in parallel, the total voltage across the combination will be the same as a single battery, which is 3V.
The total current flowing through the combination will be the sum of the currents flowing through each battery, which can be calculated using Ohm's Law:
Voltage = Current × Resistance
3V = INorton × 1Ω
Therefore, the Norton current, INorton, is 3A.
3. Calculate the Norton equivalent resistance, RNorton:
In a parallel connection, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances. Since the two batteries have the same resistance of 1Ω, the total resistance will be half of that, which is 0.5Ω.
Therefore, the Norton equivalent resistance, RNorton, is 0.5Ω.
4. Now you have obtained both the Norton current, INorton, and the Norton equivalent resistance, RNorton.
The Norton equivalent circuit can be represented as a current source connected in parallel with a resistor:
- A current source with a value of 3A (INorton).
- A resistor with a value of 0.5Ω (RNorton).
By following these steps, you can determine the Norton equivalent circuit of the combination of two identical 3V, 1 ohm batteries connected in parallel.