How to Find Resistance When Power and Voltage is Given: A Comprehensive Guide

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Understanding how to find resistance when power and voltage are given is crucial in the field of electrical circuits and is an essential concept in physics. This knowledge enables us to calculate the resistance of a circuit component, such as a resistor or a wire, when we know the power dissipated and the voltage across it. In this blog post, we will explore the relationship between power, voltage, and resistance, and learn how to calculate resistance using the relevant formulas and step-by-step examples.

The Relationship between Power, Voltage, and Resistance

The Power Resistance Voltage Formula

To begin our exploration, we need to understand the basic formula that relates power, resistance, and voltage. According to Ohm’s Law, the power dissipated in an electrical component can be calculated using the formula:

$पी = \frac{V^2}{R}$

जहां $P$ वाट में शक्ति का प्रतिनिधित्व करता है, $V$ represents the voltage in volts, and $R$ represents the resistance in ohms.

This formula tells us that the power dissipated in a component is directly proportional to the square of the voltage and inversely proportional to the resistance.

How Power, Resistance, and Voltage Interact

Understanding the relationship between power, resistance, and voltage is crucial in circuit analysis. Here’s how they interact:

Power and Voltage: The power dissipated in a circuit component increases as the voltage across it increases. This means that if the voltage doubles, the power quadruples, assuming the resistance remains constant.
Power and Resistance: The power dissipated in a component decreases as the resistance increases. This means that if the resistance doubles, the power decreases to one-fourth, assuming the voltage remains constant.
Voltage and Resistance: The voltage across a component increases as the resistance increases, assuming the power remains constant. This relationship is known as voltage division.

यह भी देखें वोल्टेज और प्रतिरोध के साथ बिजली कैसे खोजें: एक व्यापक मार्गदर्शिका

Understanding these interactions is essential for circuit design, analysis, and troubleshooting.

How to Calculate Resistance when Power and Voltage are Given

Now that we understand the relationship between power, resistance, and voltage, let’s dive into the step-by-step process of calculating resistance when power and voltage are given.

Step-by-Step Guide to Calculate Resistance

resistance when power and voltage is given 2

Identify the known values: Determine the given values for power (P) and voltage (V).
Rearrange the power formula: Rearrange the power formula to solve for resistance (R). The rearranged formula is:

$R = \frac{V^2}{P}$

Substitute the known values: Substitute the known values of power and voltage into the rearranged formula.
Calculate the resistance: Perform the necessary calculations to find the resistance.

Worked-out Examples of Finding Resistance

Let’s work through a couple of examples to illustrate how to find resistance when power and voltage are given.

उदाहरण 1:

Suppose we have a circuit component with a power dissipation of 50 watts and a voltage across it of 10 volts. Let’s find the resistance.

Step 1: Known values – Power (P) = 50 watts, Voltage (V) = 10 volts.

Step 2: Rearranged formula – $R = \frac{V^2}{P}$ .

Step 3: Substituting values – $R = \frac{10^2}{50}$ .

Step 4: Calculation – $R = \frac{100}{50} = 2$ ओम।

Therefore, the resistance of the circuit component is 2 ohms.

उदाहरण 2:

Consider a different circuit component with a power dissipation of 100 watts and a voltage across it of 5 volts. Let’s calculate the resistance.

Step 1: Known values – Power (P) = 100 watts, Voltage (V) = 5 volts.

Step 2: Rearranged formula – $R = \frac{V^2}{P}$ .

Step 3: Substituting values – $R = \frac{5^2}{100}$ .

Step 4: Calculation – $R = \frac{25}{100} = 0.25$ ओम।

Therefore, the resistance of the circuit component is 0.25 ohms.

यह भी देखें फ़्यूज़न-संचालित अंतरिक्ष यान में ऊर्जा का अनुमान कैसे लगाएं: एक व्यापक मार्गदर्शिका

By following these step-by-step instructions, you can easily calculate the resistance when power and voltage are given.

सामान्य गलतियाँ और भ्रांतियाँ

What Happens to Resistance when Voltage and Current Increases

One common misconception is that the resistance of a component increases when the voltage or current across it increases. However, this is not true. Resistance remains constant unless the physical properties of the component, such as temperature, change. An increase in voltage or current may result in an increase in power dissipation, but it does not affect the resistance itself.

सामान्य गणना त्रुटियों से बचना

When calculating resistance using the power and voltage values, it’s important to be mindful of potential calculation errors. Here are a few common mistakes to avoid:

Squaring the wrong value: Ensure that you square the voltage value, not the resistance value when using the formula.
Incorrect unit conversions: Double-check the units of power, voltage, and resistance to ensure they are consistent throughout the calculation.
Rounding errors: When performing calculations, be mindful of rounding errors that may affect the final result. It’s best to carry out calculations with full precision and round the final answer to the appropriate number of significant figures.

By being aware of these common mistakes, you can accurately calculate resistance and avoid errors in your calculations.

Numerical Problems on How to find resistance when power and voltage is given

समस्या 1:

एक सर्किट का वोल्टेज होता है $V = 12$ volts and power of $पी = 48$ watts. Find the resistance of the circuit.

उपाय:

resistance when power and voltage is given 3

दिया हुआ:
वोल्टेज, $V = 12$ वोल्ट
शक्ति, $पी = 48$ वाट

We know that power is related to voltage and resistance by the formula:
$पी = \frac{{V^2}}{R}$

यह भी देखें 23 पूरी तरह से बेलोचदार टक्कर के उदाहरण: विस्तृत तथ्य और अक्सर पूछे जाने वाले प्रश्न

Rearranging the formula to find the resistance:
$R = \frac{{V^2}}{P} = \frac{{12^2}}{48} = \frac{144}{48} = 3$

Therefore, the resistance of the circuit is $3$ ओम।

समस्या 2:

In a circuit, the voltage is $V = 24$ volts and the power is $पी = 144$ watts. Determine the resistance of the circuit.

उपाय:

दिया हुआ:
वोल्टेज, $V = 24$ वोल्ट
शक्ति, $पी = 144$ वाट

सूत्र का उपयोग करना:
$पी = \frac{{V^2}}{R}$

We can rearrange the formula to solve for resistance:
$R = \frac{{V^2}}{P} = \frac{{24^2}}{144} = \frac{{576}}{144} = 4$

Hence, the resistance of the circuit is $4$ ओम।

समस्या 3:

The voltage in a circuit is $V = 10$ volts and the power is $पी = 25$ watts. Calculate the resistance of the circuit.

उपाय:

दिया हुआ:
वोल्टेज, $V = 10$ वोल्ट
शक्ति, $पी = 25$ वाट

सूत्र का उपयोग करना:
$पी = \frac{{V^2}}{R}$

Solving for resistance:
$R = \frac{{V^2}}{P} = \frac{{10^2}}{25} = \frac{{100}}{25} = 4$

Therefore, the resistance of the circuit is $4$ ओम।

यह भी पढ़ें:

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