Understanding Resistors in Parallel

Oct 13, 2025 by magicalceylontours.com 125 views

Introduction

When dealing with electrical circuits, understanding the behavior of resistors in series and parallel configurations is crucial. In this scenario, we have a 12-volt battery connected across two resistors in parallel, with $R_1 = 1 \, \text{k}\Omega$ and $R_2 = 2 \, \text{k}\Omega$ . The question at hand is to determine the amount of current that will flow through $R_2$ . To tackle this problem, we need to apply the principles of Ohm's law and the properties of resistors in parallel configurations.

Understanding Resistors in Parallel

When resistors are connected in parallel, the voltage across each resistor is the same, but the current through each resistor can vary. The total resistance of the circuit is determined by the formula:

\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2}

In this case, we have:

\frac{1}{R_{\text{total}}} = \frac{1}{1 \, \text{k}\Omega} + \frac{1}{2 \, \text{k}\Omega}

Calculating Total Resistance

To find the total resistance, we can simplify the equation:

\frac{1}{R_{\text{total}}} = \frac{2}{2 \, \text{k}\Omega} + \frac{1}{2 \, \text{k}\Omega}

\frac{1}{R_{\text{total}}} = \frac{3}{2 \, \text{k}\Omega}

R_{\text{total}} = \frac{2 \, \text{k}\Omega}{3}

R_{\text{total}} = 666.67 \, \Omega

Applying Ohm's Law

Now that we have the total resistance, we can apply Ohm's law to find the current flowing through $R_2$ . Ohm's law states that:

I = \frac{V}{R}

In this case, the voltage is 12 volts, and the resistance is $R_{\text{total}} = 666.67 \, \Omega$ . However, we are interested in finding the current through $R_2$ , not the total current. To do this, we need to find the current through $R_2$ using the voltage and the resistance of $R_2$ .

Calculating Current Through R2

The current through $R_2$ can be found using the formula:

I_2 = \frac{V}{R_2}

I_2 = \frac{12 \, \text{V}}{2 \, \text{k}\Omega}

I_2 = 6 \, \text{mA}

Conclusion

In conclusion, when a 12-volt battery is connected across two resistors in parallel, with $R_1 = 1 \, \text{k}\Omega$ and $R_2 = 2 \, \text{k}\Omega$ , the current flowing through $R_2$ is 6 mA. This is determined by applying Ohm's law and the properties of resistors in parallel configurations.

Discussion

The calculation of current through $R_2$ is a straightforward application of Ohm's law. However, it's essential to understand the properties of resistors in parallel configurations to tackle more complex problems. In this scenario, we assumed that the resistors are ideal and have no internal resistance. In real-world scenarios, resistors may have internal resistance, which can affect the overall behavior of the circuit.

Final Answer

The final answer is: 6 mA

Introduction

In our previous article, we explored the concept of a 12-volt battery connected across two resistors in parallel, with $R_1 = 1 \, \text{k}\Omega$ and $R_2 = 2 \, \text{k}\Omega$ . We calculated the current flowing through $R_2$ to be 6 mA. In this Q&A article, we'll address some common questions and provide additional insights into the behavior of resistors in parallel configurations.

Q: What is the total resistance of the circuit?

A: The total resistance of the circuit is determined by the formula:

\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2}

In this case, we have:

\frac{1}{R_{\text{total}}} = \frac{1}{1 \, \text{k}\Omega} + \frac{1}{2 \, \text{k}\Omega}

Simplifying the equation, we get:

R_{\text{total}} = \frac{2 \, \text{k}\Omega}{3}

R_{\text{total}} = 666.67 \, \Omega

Q: Why do we need to calculate the total resistance?

A: Calculating the total resistance is essential to determine the current flowing through each resistor in the circuit. By knowing the total resistance, we can apply Ohm's law to find the current through each resistor.

Q: Can we use the formula for series resistors to calculate the total resistance?

A: No, we cannot use the formula for series resistors to calculate the total resistance. The formula for series resistors is:

R_{\text{total}} = R_1 + R_2

However, this formula is only applicable when resistors are connected in series, not in parallel.

Q: How does the current flowing through $R_2$ change if we increase the voltage?

A: If we increase the voltage, the current flowing through $R_2$ will also increase. This is because Ohm's law states that:

I = \frac{V}{R}

If we increase the voltage, the current will increase proportionally, assuming the resistance remains constant.

Q: What happens if we decrease the resistance of $R_2$ ?

A: If we decrease the resistance of $R_2$ , the current flowing through $R_2$ will increase. This is because the resistance is inversely proportional to the current, according to Ohm's law.

Q: Can we use the formula for parallel resistors to calculate the current flowing through $R_2$ ?

A: Yes, we can use the formula for parallel resistors to calculate the current flowing through $R_2$ . The formula is:

I_2 = \frac{V}{R_2}

In this case, we have:

I_2 = \frac{12 \, \text{V}}{2 \, \text{k}\Omega}

I_2 = 6 \, \text{mA}

Conclusion

In conclusion, understanding the behavior of resistors in parallel configurations is crucial to tackle complex electrical circuits. By applying Ohm's law and the properties of resistors in parallel configurations, we can calculate the current flowing through each resistor in the circuit.

Final Answer

The final answer is: 6 mA