A Parallel Circuit Consists Of Three Resistors: - $R1 = 30 \, \text{ohms}$- $R2 = 15 \, \text{ohms}$- $R3 = 10 \, \text{ohms}$The Current Through $R2$ Is 4 Amperes. What Is The Source Voltage?A. 20 Volts B. 60 Volts

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Introduction

In the world of electronics, understanding the behavior of circuits is crucial for designing and analyzing complex systems. One of the fundamental concepts in circuit analysis is the study of parallel circuits. A parallel circuit is a type of circuit where multiple branches are connected between the same two points, allowing the current to flow through each branch independently. In this article, we will explore a parallel circuit consisting of three resistors and determine the source voltage given the current through one of the resistors.

The Parallel Circuit

A parallel circuit consists of three resistors: R1 = 30 ohms, R2 = 15 ohms, and R3 = 10 ohms. The current through R2 is given as 4 amperes. To determine the source voltage, we need to understand the relationship between the resistors and the current flowing through them.

Ohm's Law

Ohm's Law states that the current flowing through a conductor is directly proportional to the voltage applied across it, and inversely proportional to the resistance of the conductor. Mathematically, this can be expressed as:

I = V/R

where I is the current, V is the voltage, and R is the resistance.

Applying Ohm's Law to the Parallel Circuit

Since the resistors are connected in parallel, the voltage across each resistor is the same. Let's denote this voltage as V. Using Ohm's Law, we can write the following equations for each resistor:

I1 = V/R1 I2 = V/R2 I3 = V/R3

We are given that the current through R2 is 4 amperes, so we can write:

I2 = 4 = V/R2

Determining the Source Voltage

To determine the source voltage, we need to find the total current flowing through the circuit. Since the resistors are connected in parallel, the total current is the sum of the currents flowing through each resistor:

I_total = I1 + I2 + I3

We can substitute the expressions for I1, I2, and I3 from the previous section:

I_total = V/R1 + V/R2 + V/R3

Simplifying the Expression

Since the voltage across each resistor is the same, we can simplify the expression by factoring out V:

I_total = V/R1 + V/R2 + V/R3 = V(1/R1 + 1/R2 + 1/R3)

Substituting the Values

Now, we can substitute the values of R1, R2, and R3 into the expression:

I_total = V(1/30 + 1/15 + 1/10) = V(0.0333 + 0.0667 + 0.1) = V(0.2)

Finding the Total Current

We are given that the current through R2 is 4 amperes. Since the resistors are connected in parallel, the total current is the sum of the currents flowing through each resistor. However, we are not given the currents through R1 and R3. To find the total current, we need to use the fact that the voltage across each resistor is the same.

Using the Current Through R2 to Find the Total Current

Since the voltage across each resistor is the same, we can use the current through R2 to find the total current. We know that:

I2 = 4 = V/R2

We can rearrange this equation to solve for V:

V = I2 * R2 = 4 * 15 = 60

Conclusion

In this article, we analyzed a parallel circuit consisting of three resistors and determined the source voltage given the current through one of the resistors. We used Ohm's Law and the properties of parallel circuits to derive an expression for the total current and then used the current through R2 to find the source voltage. The source voltage was found to be 60 volts.

Frequently Asked Questions

  • What is a parallel circuit? A parallel circuit is a type of circuit where multiple branches are connected between the same two points, allowing the current to flow through each branch independently.
  • What is Ohm's Law? Ohm's Law states that the current flowing through a conductor is directly proportional to the voltage applied across it, and inversely proportional to the resistance of the conductor.
  • How do you determine the source voltage in a parallel circuit? To determine the source voltage in a parallel circuit, you need to use Ohm's Law and the properties of parallel circuits to derive an expression for the total current and then use the current through one of the resistors to find the source voltage.

References

Introduction

In the world of electronics, understanding the behavior of circuits is crucial for designing and analyzing complex systems. One of the fundamental concepts in circuit analysis is the study of parallel circuits. A parallel circuit is a type of circuit where multiple branches are connected between the same two points, allowing the current to flow through each branch independently. In this article, we will explore a parallel circuit consisting of three resistors and determine the source voltage given the current through one of the resistors.

The Parallel Circuit

A parallel circuit consists of three resistors: R1 = 30 ohms, R2 = 15 ohms, and R3 = 10 ohms. The current through R2 is given as 4 amperes. To determine the source voltage, we need to understand the relationship between the resistors and the current flowing through them.

Ohm's Law

Ohm's Law states that the current flowing through a conductor is directly proportional to the voltage applied across it, and inversely proportional to the resistance of the conductor. Mathematically, this can be expressed as:

I = V/R

where I is the current, V is the voltage, and R is the resistance.

Applying Ohm's Law to the Parallel Circuit

Since the resistors are connected in parallel, the voltage across each resistor is the same. Let's denote this voltage as V. Using Ohm's Law, we can write the following equations for each resistor:

I1 = V/R1 I2 = V/R2 I3 = V/R3

We are given that the current through R2 is 4 amperes, so we can write:

I2 = 4 = V/R2

Determining the Source Voltage

To determine the source voltage, we need to find the total current flowing through the circuit. Since the resistors are connected in parallel, the total current is the sum of the currents flowing through each resistor:

I_total = I1 + I2 + I3

We can substitute the expressions for I1, I2, and I3 from the previous section:

I_total = V/R1 + V/R2 + V/R3

Simplifying the Expression

Since the voltage across each resistor is the same, we can simplify the expression by factoring out V:

I_total = V/R1 + V/R2 + V/R3 = V(1/R1 + 1/R2 + 1/R3)

Substituting the Values

Now, we can substitute the values of R1, R2, and R3 into the expression:

I_total = V(1/30 + 1/15 + 1/10) = V(0.0333 + 0.0667 + 0.1) = V(0.2)

Finding the Total Current

We are given that the current through R2 is 4 amperes. Since the resistors are connected in parallel, the total current is the sum of the currents flowing through each resistor. However, we are not given the currents through R1 and R3. To find the total current, we need to use the fact that the voltage across each resistor is the same.

Using the Current Through R2 to Find the Total Current

Since the voltage across each resistor is the same, we can use the current through R2 to find the total current. We know that:

I2 = 4 = V/R2

We can rearrange this equation to solve for V:

V = I2 * R2 = 4 * 15 = 60

Conclusion

In this article, we analyzed a parallel circuit consisting of three resistors and determined the source voltage given the current through one of the resistors. We used Ohm's Law and the properties of parallel circuits to derive an expression for the total current and then used the current through R2 to find the source voltage. The source voltage was found to be 60 volts.

Frequently Asked Questions

Q: What is a parallel circuit?

A: A parallel circuit is a type of circuit where multiple branches are connected between the same two points, allowing the current to flow through each branch independently.

Q: What is Ohm's Law?

A: Ohm's Law states that the current flowing through a conductor is directly proportional to the voltage applied across it, and inversely proportional to the resistance of the conductor.

Q: How do you determine the source voltage in a parallel circuit?

A: To determine the source voltage in a parallel circuit, you need to use Ohm's Law and the properties of parallel circuits to derive an expression for the total current and then use the current through one of the resistors to find the source voltage.

Q: What is the relationship between the resistors in a parallel circuit?

A: In a parallel circuit, the voltage across each resistor is the same, but the current flowing through each resistor can be different.

Q: How do you calculate the total current in a parallel circuit?

A: To calculate the total current in a parallel circuit, you need to use the expression I_total = V/R1 + V/R2 + V/R3, where V is the voltage across each resistor.

Q: What is the significance of the current through R2 in this problem?

A: The current through R2 is used to find the total current in the circuit, which is then used to determine the source voltage.

Q: What is the source voltage in this problem?

A: The source voltage in this problem is 60 volts.

References

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