How to Find Voltage Across Resistor:Several Approaches And Problems Example

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How to Find Voltage Across a Resistor

how to find voltage across resistor
Image by Circuit-fantasist – Wikimedia Commons, Wikimedia Commons, Licensed under CC BY-SA 4.0.

When working with electrical circuits, it is essential to understand how to find the voltage across a resistor. The voltage across a resistor refers to the potential difference or drop in voltage that occurs across the resistor when electric current flows through it. In this blog post, we will explore various methods to calculate and measure voltage across a resistor. We will also provide practical examples to help solidify your understanding.

How to Calculate Voltage Across a Resistor

voltage across resistor 1

Using Ohm’s Law to Calculate Voltage

Ohm’s Law is a fundamental principle in electronics that relates voltage, current, and resistance. According to Ohm’s Law, the voltage across a resistor (V) can be calculated by multiplying the current (I) flowing through the resistor by its resistance (R). Mathematically, this can be expressed as:

V = I times R

Let’s say we have a circuit with a resistor of 10 ohms and a current of 2 amps flowing through it. We can calculate the voltage across the resistor using Ohm’s Law as follows:

V = 2 , text{A} times 10 , Omega = 20 , text{V}

Therefore, the voltage across the resistor is 20 volts.

Calculating Voltage without Current

Sometimes, you may need to find the voltage across a resistor without knowing the current flowing through it. In such cases, you can use the voltage divider equation. The voltage divider equation allows you to calculate the voltage across a resistor based on the ratio of its resistance to the total resistance in the circuit.

The voltage across a specific resistor (Vr) can be calculated using the following formula:

Vr = frac{Rr}{Rt} times Vt

Where:
– Vr is the voltage across the resistor of interest.
– Rr is the resistance of the resistor of interest.
– Rt is the total resistance in the circuit.
– Vt is the total voltage across the circuit.

For example, consider a circuit with two resistors in series. The total resistance is 20 ohms, and the total voltage across the circuit is 10 volts. If one of the resistors has a value of 5 ohms and you want to find the voltage across it, you can use the voltage divider equation:

Vr = frac{5 , Omega}{20 , Omega} times 10 , text{V} = 2.5 , text{V}

Hence, the voltage across the 5-ohm resistor is 2.5 volts.

Calculating Voltage across a Resistor in Series

In a series circuit, the total voltage is divided among the resistors based on their individual resistance values. The voltage across each resistor is proportional to its resistance. To calculate the voltage across a specific resistor in a series circuit, you can use the following formula:

Vr = frac{Rr}{Rt} times Vt

Where:
– Vr is the voltage across the resistor of interest.
– Rr is the resistance of the resistor of interest.
– Rt is the total resistance in the circuit.
– Vt is the total voltage across the circuit.

Let’s consider a series circuit with three resistors, R1 = 5 ohms, R2 = 10 ohms, and R3 = 15 ohms. The total voltage across the circuit is 12 volts. If we want to find the voltage across R2, we can use the formula:

V2 = frac{R2}{Rt} times Vt = frac{10 , Omega}{5 , Omega + 10 , Omega + 15 , Omega} times 12 , text{V} = 4 , text{V}

Therefore, the voltage across resistor R2 is 4 volts.

Calculating Voltage across a Resistor in Parallel

In a parallel circuit, the voltage across each resistor is the same, while the current is divided based on the resistance values. To calculate the voltage across a resistor in a parallel circuit, you can use the following formula:

Vr = Vt

Where:
– Vr is the voltage across the resistor of interest.
– Vt is the total voltage across the circuit.

Consider a parallel circuit with three resistors, each having a resistance of 10 ohms. The total voltage across the circuit is 15 volts. If we want to find the voltage across any of the resistors, we can use the formula:

Vr = Vt = 15 , text{V}

Hence, the voltage across each resistor is 15 volts.

How to Measure Voltage Across a Resistor

Using a Multimeter to Measure Voltage

A multimeter is a versatile tool used to measure various electrical quantities, including voltage. To measure voltage across a resistor using a multimeter, follow these steps:

  1. Set the multimeter to the voltage measurement mode.
  2. Connect the multimeter leads in parallel with the resistor, ensuring correct polarity.
  3. Read the voltage value displayed on the multimeter.

Make sure to select an appropriate voltage range on the multimeter to get an accurate reading.

Using an Oscilloscope to Measure Voltage

An oscilloscope is a more advanced instrument used to visualize and measure electrical waveforms. To measure voltage across a resistor using an oscilloscope, you can follow these steps:

  1. Connect the oscilloscope probes in parallel with the resistor, ensuring correct polarity.
  2. Adjust the oscilloscope settings to display the voltage waveform.
  3. Read the voltage value from the oscilloscope screen.

An oscilloscope provides a visual representation of the voltage waveform, allowing you to analyze the signal’s characteristics.

Measuring Voltage in LTSpice

LTSpice is a popular software used for circuit simulation. It allows you to simulate and measure various electrical quantities, including voltage. To measure voltage across a resistor using LTSpice, you can follow these steps:

  1. Create a circuit diagram in LTSpice, including the resistor of interest.
  2. Run the simulation.
  3. Use the voltage probe tool to measure the voltage across the resistor.
  4. Read the voltage value from the simulation results.

LTSpice provides an accurate representation of circuit behavior, making it a valuable tool for voltage measurements.

Practical Examples of Finding Voltage Across a Resistor

Finding Voltage in a Combination Circuit

Consider a combination circuit with resistors in both series and parallel configurations. To find the voltage across a specific resistor, apply the relevant formulas and techniques discussed earlier for series and parallel circuits.

Finding Voltage across Each Resistor in a Series Circuit

In a series circuit, the voltage across each resistor is proportional to its resistance. To find the voltage across each resistor, you can use the formula:

Vr = frac{Rr}{Rt} times Vt

Apply this formula for each resistor in the series circuit to determine the voltage across each one.

Finding Voltage across Parallel Resistors

In a parallel circuit, the voltage across each resistor is the same. To find the voltage across each resistor, simply measure the voltage at any point in the circuit.

Finding Voltage across Two Resistors

Consider a circuit with two resistors connected in series. To find the voltage across each resistor, use the voltage divider equation:

Vr = frac{Rr}{Rt} times Vt

Apply this formula separately for each resistor to calculate the voltage across them.

By applying the appropriate formulas and techniques, you can find the voltage across any resistor in various circuit configurations.

Remember, understanding how to find the voltage across a resistor is crucial for analyzing and designing electrical circuits. Whether you are an electronics enthusiast, a student, or a professional, this knowledge will greatly enhance your understanding and ability to work with circuits effectively.

Now that you have learned different methods to calculate and measure voltage across a resistor, you are well-equipped to tackle various circuit challenges. Keep practicing, and soon you’ll become a master at analyzing voltage drops and understanding circuit behavior.

Happy exploring and experimenting!

How is the voltage drop across a resistor related to understanding voltage drop for cable?

The voltage drop across a resistor can be likened to understanding voltage drop for cable. When a current passes through a resistor, a voltage drop occurs across it according to Ohm’s Law. Similarly, when electrical current flows through a cable, there will also be a voltage drop along its length due to the cable’s resistance. This understanding of voltage drop for cable is crucial in electrical engineering, as it helps in determining the suitable cable size and minimizing power losses. To gain a deeper insight into voltage drop for cable, you can refer to the article on Understanding voltage drop for cable.

Numerical Problems on how to find voltage across resistor

Problem 1:

In a circuit, a resistor with resistance R = 5 , Omega is connected to a voltage source with an electromotive force emf) of ( V = 12 , V . Find the voltage across the resistor.

Solution:
To find the voltage across the resistor, we can use Ohm’s Law, which states that the voltage across a resistor is equal to the current flowing through it multiplied by its resistance.

Ohm’s Law: V = I cdot R

We need to find the current flowing through the circuit. To do this, we can use another formula, which relates the current to the emf and the total resistance in the circuit.

Formula: I = frac{V}{R_{text{total}}}

Since there is only one resistor in the circuit, the total resistance is equal to the resistance of the resistor.

Substituting the given values into the formulas, we get:

I = frac{12,V}{5,Omega} = 2.4,A

V = I cdot R = 2.4,A cdot 5,Omega = 12,V

Therefore, the voltage across the resistor is 12 V.

Problem 2:

voltage across resistor 3

In a circuit, a resistor with resistance R = 10 , Omega is connected to a battery with an electromotive force emf) of ( V = 24 , V . Find the current flowing through the resistor.

Solution:
To find the current flowing through the resistor, we can again use Ohm’s Law, which states that the current flowing through a resistor is equal to the voltage across it divided by its resistance.

Ohm’s Law: I = frac{V}{R}

Substituting the given values into the formula, we get:

I = frac{24,V}{10,Omega} = 2.4,A

Therefore, the current flowing through the resistor is 2.4 A.

Problem 3:

how to find voltage across resistor
Image by Circuit-fantasist – Wikimedia Commons, Wikimedia Commons, Licensed under CC BY-SA 4.0.
voltage across resistor 2

In a circuit, a resistor with resistance R = 8 , Omega is connected to a battery with an electromotive force emf) of ( V = 16 , V . Find the power dissipated by the resistor.

Solution:
To find the power dissipated by the resistor, we can use the formula:

P = frac{V^2}{R}

Substituting the given values into the formula, we get:

P = frac{16^2,V^2}{8,Omega} = 32,W

Therefore, the power dissipated by the resistor is 32 W.

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