प्रतिरोध और धारा के साथ शक्ति कैसे खोजें: एक व्यापक मार्गदर्शिका

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Power is an essential concept in the world of electricity. It represents the rate at which energy is transferred or transformed. Understanding how to calculate power with resistance and current is crucial in various applications, from designing circuits to calculating energy consumption. In this blog post, we will explore the relationship between power, resistance, and current, and learn how to calculate power using Ohm’s Law and the Power Law. We will also delve into advanced concepts such as power loss and power determination with resistance and voltage.

The Relationship between Power, Resistance, and Current

The Ohm’s Law

power with resistance and current 3

Before we dive into calculating power, let’s briefly revisit 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, Ohm’s Law is expressed as:

V = I \cdot R

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

द पावर लॉ

The Power Law, derived from Ohm’s Law, allows us to calculate the power dissipated or delivered in a circuit. The power is equal to the product of the current and the voltage. Mathematically, the Power Law is expressed as:

P = I \cdot V

कहा पे:
- P denotes the power,
- I represents the current flowing through the circuit, and
- V symbolizes the voltage across the circuit.

How to Calculate Power with Resistance and Current

Step-by-step Guide to Calculate Power

Now, let’s learn how to calculate power using resistance and current. Follow these steps:

  1. Determine the value of the resistance in ohms (\ओमेगा).
  2. Measure the current passing through the circuit in amperes (A).
  3. Multiply the resistance by the square of the current.
  4. The resulting value is the power dissipated or delivered in watts (W).

The formula to calculate power with resistance and current is:

पी = आई^2 \सीडॉट आर

पावर गणना पर तैयार किए गए उदाहरण

प्रतिरोध और धारा के साथ शक्ति कैसे ज्ञात करें
छवि द्वारा चेतवर्नो - विकिमीडिया कॉमन्स, विकिमीडिया कॉमन्स, CC0 के तहत लाइसेंस प्राप्त।
power with resistance and current 2

आइए अपनी समझ को पुख्ता करने के लिए कुछ उदाहरणों पर काम करें।

उदाहरण 1:
Consider a circuit with a resistance of 10 ohms and a current of 2 amperes. Calculate the power dissipated in the circuit.

उपाय:
सूत्र का उपयोग करना पी = आई^2 \सीडॉट आर, we can calculate the power as follows:

P = (2 \, \text{A})^2 \cdot 10 \, \Omega = 4 \, \text{W}

इसलिए, परिपथ में व्यय हुई शक्ति 4 वाट है।

उदाहरण 2:
Suppose a circuit has a resistance of 5 ohms, and the current passing through it is 3 amperes. Determine the power delivered in the circuit.

उपाय:
सूत्र का उपयोग करना पी = आई^2 \सीडॉट आर, we can calculate the power as follows:

P = (3 \, \text{A})^2 \cdot 5 \, \Omega = 45 \, \text{W}

Hence, the power delivered in the circuit is 45 watts.

By following these step-by-step calculations, we can accurately determine the power dissipated or delivered in a circuit using resistance and current values.

उन्नत अवधारणाएँ और अनुप्रयोग

प्रतिरोध और धारा के साथ शक्ति कैसे ज्ञात करें
छवि द्वारा चेतवर्नो - विकिमीडिया कॉमन्स, विकिमीडिया कॉमन्स, CC0 के तहत लाइसेंस प्राप्त।

How to Calculate Power Loss with Resistance and Current

In some cases, it is important to calculate the power loss in a circuit. Power loss refers to the energy dissipated as heat due to the resistance in the circuit. To calculate power loss, we use the formula:

P_{\text{नुकसान}} = ​​I^2 \cdot R

कहा पे:
- पी_{\पाठ{नुकसान}} represents the power loss in watts (W),
- I is the current flowing through the circuit in amperes (A), and
- R denotes the resistance in ohms (\ओमेगा).

How to Determine Power with Resistance and Voltage

power with resistance and current 1

In addition to calculating power with resistance and current, we can also determine power using resistance and voltage. The formula to calculate power with resistance and voltage is:

पी = \frac{V^2}{R}

कहा पे:
- P denotes the power in watts (W),
- V represents the voltage across the circuit in volts (V), and
- R symbolizes the resistance in ohms (\ओमेगा).

Numerical Problems on How to find power with resistance and current

समस्या 1

एक सर्किट का प्रतिरोध होता है R = 10\Omega और एक धारा मैं = २३A ए. परिपथ में व्यय हुई शक्ति का निर्धारण करें।

उपाय:

The power dissipated in a circuit can be calculated using the formula:

P = I^2 \गुना R

दिए गए मानों को जोड़ने पर, हमारे पास है:

P = (2A)^2 \times 10\Omega

सरल बनाना,

P = 4A^2 \times 10\Omega

इसलिए, सर्किट में बिजली का क्षय होता है 40 वत्स।

समस्या 2

In a circuit, the power dissipated is पी = 75 Watts and the resistance is R = 5\Omega. Determine the current flowing through the circuit.

उपाय:

To find the current flowing through the circuit, we can rearrange the formula for power:

P = I^2 \गुना R

समीकरण के दोनों पक्षों को विभाजित करने पर R, हम पाते हैं:

\frac{P}{R} = I^2

दिए गए मानों को जोड़ने पर, हमारे पास है:

\frac{75}{5\Omega} = I^2

सरल बनाना,

15 = I^2

दोनों पक्षों का वर्गमूल लेने पर, हम पाते हैं:

I = \sqrt{15}

Therefore, the current flowing through the circuit is approximately 3.87 एम्पीयर.

समस्या 3

A circuit has a power dissipation of पी = 200 Watts and a current of मैं = २३A ए. Determine the resistance of the circuit.

उपाय:

To find the resistance of the circuit, we can rearrange the formula for power:

P = I^2 \गुना R

समीकरण के दोनों पक्षों को विभाजित करने पर I^2, हम पाते हैं:

\frac{P}{I^2} = R

दिए गए मानों को जोड़ने पर, हमारे पास है:

\frac{200}{(5A)^2} = R

सरल बनाना,

\frac{200}{25A^2} = R

इसलिए, सर्किट का प्रतिरोध है 8 ओह्स।

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