How to Find Power with Voltage and Resistance: A Comprehensive Guide

Understanding the relationship between power, voltage, and resistance is essential when working with electrical circuits. In this blog post, we will delve into the topic of how to find power with voltage and resistance. We will explore the fundamental principles, equations, and calculations involved in determining power, and provide step-by-step instructions along with examples to make the concept clearer. So let’s get started!

The Relationship Between Power, Voltage, and Resistance

Before we dive into the calculations, it is crucial to understand the fundamental laws that govern the relationship between power, voltage, and resistance. Two key principles that play a significant role in this context are Ohm’s Law and the Power Law.

ओम का नियम

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, Ohm’s Law can be expressed as:

$वी = आईआर$

कहा पे:
- $V$ कंडक्टर के पार वोल्टेज का प्रतिनिधित्व करता है,
- $I$ denotes the electric current flowing through the conductor, and
- $R$ stands for the resistance of the conductor.

द पावर लॉ

The Power Law, also known as Joule’s Law, illustrates the relationship between power, voltage, and current. According to this law, the power dissipated or consumed by an electrical component can be calculated using the following formula:

$पी = चतुर्थ$

कहा पे:
- $P$ represents the power consumed or dissipated by the electrical component,
- $I$ denotes the electric current flowing through the component, and
- $V$ represents the voltage across the component.

Now that we have a clear understanding of these fundamental principles, let’s move on to the next section and learn how to calculate power using voltage and resistance.

How to Calculate Power with Voltage and Resistance

छवि द्वारा चेतवर्नो - विकिमीडिया कॉमन्स, विकिमीडिया कॉमन्स, CC0 के तहत लाइसेंस प्राप्त।

वोल्टेज और प्रतिरोध के साथ बिजली कैसे खोजें — छवि द्वारा चेतवर्नो - विकिमीडिया कॉमन्स, विकिमीडिया कॉमन्स, CC0 के तहत लाइसेंस प्राप्त।

Calculating power using voltage and resistance is relatively straightforward. To guide you through the process, let’s follow this step-by-step guide:

यह भी देखें क्वथनांक और सतह क्षेत्र: विस्तृत तथ्य

पावर की गणना करने के लिए चरण-दर-चरण मार्गदर्शिका

Start by determining the voltage $\(वी$ ) across the component. This value can be obtained directly from the circuit or calculated using Ohm’s Law $\(V = IR$ ), कहा पे $I$ is the current and $R$ is the resistance.
Once you have the voltage, determine the resistance $\(आर$ ) of the component. This information is either given or measured using an appropriate instrument.
With both the voltage and resistance values at hand, you can now apply the Power Law $\(P = IV$ ) to find the power $\(पी$ ) dissipated or consumed by the component.

By following these steps, you can easily calculate the power using the voltage and resistance values of an electrical component. Let’s solidify this concept with some worked-out examples.

पावर गणना पर तैयार किए गए उदाहरण

उदाहरण 1:
Suppose a circuit has a voltage of 12 volts and a resistance of 4 ohms. To calculate the power dissipated in the circuit, we can use the Power Law equation:

$पी = चतुर्थ$

दिए गए मानों को प्रतिस्थापित करने पर, हमारे पास है:

$P = (12 \, \text{V}) \times \left(\frac{12 \, \text{V}}{4 \, \Omega}\right) = 36 \, \text{W}$

Therefore, the power dissipated in the circuit is 36 Watts.

उदाहरण 2:
Consider a resistor with a voltage drop of 6 volts and a resistance of 2 ohms. To find the power dissipated by the resistor, we can use the same Power Law equation:

$पी = चतुर्थ$

दिए गए मानों को प्रतिस्थापित करने पर, हमें प्राप्त होता है:

$P = (6 \, \text{V}) \times \left(\frac{6 \, \text{V}}{2 \, \Omega}\right) = 18 \, \text{W}$

Hence, the power dissipated by the resistor is 18 Watts.

These examples demonstrate how to calculate power using voltage and resistance values. Now that we understand how to find power, let’s explore how we can determine other parameters when voltage and resistance are given.

How to Find Other Parameters with Given Values

Having a grasp of how to calculate power, we can also determine other key parameters in electrical circuits when the voltage and resistance values are known. Let’s take a look at how to find current, resistance, and voltage using these given values.

How to Calculate Current with Voltage and Resistance

Using Ohm’s Law $\(V = IR$ ), we can rearrange the equation to solve for current $\(मैं$ ):

यह भी देखें वायु प्रतिरोध को क्या प्रभावित करता है और कैसे? 7 तथ्य जो आपको जानना जरूरी है!

$मैं = \frac{V}{R}$

By dividing the voltage $\(वी$ ) by the resistance $\(आर$ ), we can determine the current flowing through the circuit.

How to Calculate Resistance with Voltage and Power

To calculate the resistance $\(आर$ ) when the voltage $\(वी$ ) and power $\(पी$ ) are given, we rearrange the Power Law equation $\(P = IV$ ) to solve for resistance:

$R = \frac{V}{I}$

By dividing the voltage $\(वी$ ) by the current $\(मैं$ ), we can determine the resistance of the circuit.

How to Calculate Voltage Using Power and Resistance

If we have the power $\(पी$ ) और प्रतिरोध $\(आर$ ) values and want to find the voltage $\(वी$ ), we rearrange the Power Law equation $\(P = IV$ ) to solve for voltage:

$वी = \frac{P}{I}$

By dividing the power $\(पी$ ) by the current $\(मैं$ ), we can determine the voltage across the circuit.

By applying these formulas, we can find other parameters in electrical circuits when voltage and resistance values are provided.

In this blog post, we explored the concept of finding power using voltage and resistance in electrical circuits. We learned about Ohm’s Law and the Power Law, which form the foundation for understanding this relationship. Additionally, we discussed step-by-step instructions for calculating power and provided worked-out examples to solidify the concepts. Furthermore, we discovered how to find other parameters such as current, resistance, and voltage using given values. Armed with this knowledge, you can now confidently analyze and calculate power in electrical circuits by leveraging voltage and resistance.

Numerical Problems on How to find power with voltage and resistance

A circuit has a voltage of 12 volts and a resistance of 4 ohms. Calculate the power dissipated in the circuit.

उपाय:

Given: Voltage (V) = 12 volts and Resistance (R) = 4 ohms.

शक्ति (पी) की गणना करने का सूत्र इस प्रकार दिया गया है:

$पी = \frac{V^2}{R}$

दिए गए मानों को सूत्र में प्रतिस्थापित करने पर, हमें प्राप्त होता है:

$पी = \frac{12^2}{4}$

समीकरण को सरल बनाने पर, हमारे पास है:

यह भी देखें प्रक्षेप्य गति में त्वरण कैसे प्राप्त करें: एक व्यापक मार्गदर्शिका

$पी = \frac{144}{4}$

$पी = 36$

इसलिए, परिपथ में व्यय हुई शक्ति 36 वाट है।

In a circuit, the power dissipated is 50 watts and the resistance is 10 ohms. Calculate the voltage across the circuit.

उपाय:

Given: Power (P) = 50 watts and Resistance (R) = 10 ohms.

वोल्टेज (V) की गणना करने का सूत्र इस प्रकार दिया गया है:

$वी = \sqrt{P \cdot R}$

दिए गए मानों को सूत्र में प्रतिस्थापित करने पर, हमें प्राप्त होता है:

$वी = \sqrt{50 \cdot 10}$

समीकरण को सरल बनाने पर, हमारे पास है:

$वी = \sqrt{500}$

$V \approx 22.36$

Therefore, the voltage across the circuit is approximately 22.36 volts.

A circuit has a power dissipation of 75 watts and a voltage of 15 volts. Calculate the resistance in the circuit.

उपाय:

Given: Power (P) = 75 watts and Voltage (V) = 15 volts.

The formula to calculate resistance (R) is given by:

$आर = \frac{V^2}{P}$

दिए गए मानों को सूत्र में प्रतिस्थापित करने पर, हमें प्राप्त होता है:

$आर = \frac{15^2}{75}$

समीकरण को सरल बनाने पर, हमारे पास है:

$आर = \frac{225}{75}$

$आर = 3$

इसलिए, सर्किट में प्रतिरोध 3 ओम है।

यह भी पढ़ें:

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