What is Resistivity?- Formula, Unit for Class 12 & 10 in Chemistry

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What is Resistivity?

What is Resistivity? Answer to this is- Resistivity, electrical resistance of a conductor of unit cross-sectional area and unit length. A characteristic property of each material, resistivity is useful in comparing various materials on the basis of their ability to conduct electric currents. High resistivity designates poor conductors.

What is Resistivity- Unit

Resistivity, commonly symbolized by the Greek letter rho, ρ, is quantitatively equal to the resistance R of a specimen such as a wire, multiplied by its cross-sectional area A, and divided by its length l; ρ = RA/l. The unit of resistance is the ohm. In the metre-kilogram-second (mks) system, the ratio of area in square metres to length in metres simplifies to just metres. Thus, in the metre-kilogram-second system, the unit of resistivity is ohm-metre. If lengths are measured in centimetres, resistivity may be expressed in units of ohm-centimetre.

What is Resistivity- for Class 12 and 10

The resistivity of an exceedingly good electrical conductor, such as hard-drawn copper, at 20° C (68° F) is 1.77 × 10-8 ohm-metre, or 1.77 × 10-6 ohm-centimetre. At the other extreme, electrical insulators have resistivities in the range 1012 to 1020 ohm-metres.

The value of resistivity depends also on the temperature of the material; tabulations of resistivities usually list values at 20° C. Resistivity of metallic conductors generally increases with a rise in temperature; but resistivity of semiconductors, such as carbon and silicon, generally decreases with temperature rise.

Conductivity is the reciprocal of resistivity, and it, too, characterizes materials on the basis of how well electric current flows in them. The metre-kilogram-second unit of conductivity is mho per metre, or ampere per volt-metre. Good electrical conductors have high conductivities and low resistivities. Good insulators, or dielectrics, have high resistivities and low conductivities. Semiconductors have intermediate values of both.

What is Resistivity- Formula

The resistivity of a material is defined as the resistance of a conductor of material per unit length and per unit cross-sectional area at a particular temperature

It is the property of a material that demonstrates how strongly the material resists or conducts electric current. It is denoted by ρ which is called rho. The formula for resistivity is given as,

ρ = (RA)/l ⇢ (where ‘R’ is resistance, ‘A’ is the Area of cross section ,’l’ is the length)

ρ = 1/σ ⇢ (σ is the conductivity)

What is Resistivity- Derivation

Given: R = ρl/a

Where, R – Resistance,

ρ – Resistivity

l – length of material

A – Area of cross-section

Rearranging the above equation,

RA = ρl

ρl = RA

ρ = (RA)/l

What is Resistivity- SI Unit

SI unit of R = ohm

SI unit of A = m2

SI unit of l = m

SI unit of ρ = (ohm × m2)/m

ρ = ohm m

SI unit of resistivity is ‘ohm meter(Ωm)’

Factors Affecting The Resistivity

The resistivity of a conductor is directly proportional to its resistance [ρ ∝ R].

The resistivity of a conductor is directly proportional to its uniform cross-sectional area. [ρ ∝ A]. The resistivity of a conductor is inversely proportional to its length. [ρ ∝ 1/l]

Resistivity also depends upon the nature of the material and temperature as well.

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What is Resistivity- Sample Questions Examples in Chemistry

Question 1: Calculate the resistivity of a wire whose length is 30cm and the area is 0.9 m2. The resistance of that wire is 5Ω?

Solution:

R = 5Ω

l = 30 cm = o.3 m

A = 0.9m2

ρ = RA / l

ρ = (5 × 0.9)/0.3 Ωm

ρ = 15 Ωm

Therefore resistivity will be 15 Ωm

Question 2: Given that the conducting material is 4 ohm-1m-1. Calculate resistivity?

Solution:

Conductivity (σ ) = 4 ohm-1m-1

ρ = 1/ σ

ρ = 1/4 ohm m

ρ = 0.25 ohm m

So, resistivity will be 0.25 ohm m

Question 3: Why are alloys used for making standard resistors?

Solution:

Alloys have a high value of resistivity as well as low temperature coefficient of resistance.

Question 4: Name the element which has the highest resistivity and the metal which has the lowest resistivity?

Solution:

Nichrome has the highest resistivity (1.50 × 10-6 Ωm)

Question 5: Identify which has the best conductivity as given that the resistivity of copper, constantan, and silver are 1.74 × 10-8Ωm, 39.1 × 10-8Ωm, and 1.6 × 10-8Ωm respectively?

Solution:

Conductivity = 1/ resistivity

Silver has the best conductivity as it has the lowest resistivity

Question 6: Calculate the resistance of a metal wire of length 3m and 0.6 of diameter having resistance is 60 Ω?

Solution :

R = 60

Diameter = 0.6 m

Radius (r) = 0.3m

Area of cross section = πr2

A = 3.14 × (0.3 × 0.3)m2

A = 0.2826

Length (l) = 3m

ρ = RA / l

ρ = (60 × 0.2826)/3

ρ = 5.652 Ωm

What is Resistivity in Hindi?

प्रतिरोधकता क्या है? इसका उत्तर है- इकाई अनुप्रस्थ काट क्षेत्रफल तथा इकाई लम्बाई के चालक की प्रतिरोधकता, विद्युत प्रतिरोध। प्रत्येक सामग्री की एक विशिष्ट संपत्ति, प्रतिरोधकता विद्युत धाराओं के संचालन की उनकी क्षमता के आधार पर विभिन्न सामग्रियों की तुलना करने में उपयोगी होती है। उच्च प्रतिरोधकता खराब कंडक्टरों को नामित करती है।

प्रतिरोधकता क्या है? – इकाई

प्रतिरोधकता, जिसे आमतौर पर ग्रीक अक्षर rho, द्वारा दर्शाया जाता है, मात्रात्मक रूप से एक नमूने के प्रतिरोध R के बराबर होता है, जैसे कि एक तार, इसके क्रॉस-अनुभागीय क्षेत्र A से गुणा किया जाता है, और इसकी लंबाई l से विभाजित किया जाता है; = आरए / एल। प्रतिरोध की इकाई ओम है। मीटर-किलोग्राम-सेकंड (एमकेएस) प्रणाली में, वर्ग मीटर में क्षेत्रफल का मीटर में लंबाई का अनुपात केवल मीटर तक सरल हो जाता है। इस प्रकार, मीटर-किलोग्राम-सेकंड प्रणाली में, प्रतिरोधकता की इकाई ओम-मीटर है। यदि लंबाई सेंटीमीटर में मापी जाती है, तो प्रतिरोधकता ओम-सेंटीमीटर की इकाइयों में व्यक्त की जा सकती है।

प्रतिरोधकता क्या है?- कक्षा 12 और 10 के लिए

20 डिग्री सेल्सियस (68 डिग्री फारेनहाइट) पर अत्यधिक अच्छे विद्युत कंडक्टर, जैसे कठोर तांबे की प्रतिरोधकता 1.77 × 10-8 ओम-मीटर, या 1.77 × 10-6 ओम-सेंटीमीटर है। दूसरे छोर पर, विद्युत इंसुलेटर की प्रतिरोधकता 1012 से 1020 ओम-मीटर की सीमा में होती है।

प्रतिरोधकता का मान सामग्री के तापमान पर भी निर्भर करता है; प्रतिरोधकता के सारणीकरण में आमतौर पर 20 डिग्री सेल्सियस पर मान सूचीबद्ध होते हैं। धातु के कंडक्टरों की प्रतिरोधकता आमतौर पर तापमान में वृद्धि के साथ बढ़ जाती है; लेकिन कार्बन और सिलिकॉन जैसे अर्धचालकों की प्रतिरोधकता आमतौर पर तापमान बढ़ने के साथ कम हो जाती है।

चालकता प्रतिरोधकता का पारस्परिक है, और यह भी सामग्री को इस आधार पर चिह्नित करता है कि उनमें विद्युत प्रवाह कितनी अच्छी तरह से प्रवाहित होता है। चालकता की मीटर-किलोग्राम-सेकंड इकाई एमएचओ प्रति मीटर या एम्पीयर प्रति वोल्ट-मीटर है। अच्छे विद्युत कंडक्टरों में उच्च चालकता और कम प्रतिरोधकता होती है। अच्छे इंसुलेटर, या डाइलेक्ट्रिक्स में उच्च प्रतिरोधकता और कम चालकता होती है। अर्धचालकों में दोनों का मध्यवर्ती मान होता है।

प्रतिरोधकता क्या है? – सूत्र

किसी सामग्री की प्रतिरोधकता को किसी विशेष तापमान पर प्रति इकाई लंबाई और प्रति इकाई क्रॉस-सेक्शनल क्षेत्र के सामग्री के कंडक्टर के प्रतिरोध के रूप में परिभाषित किया जाता है।

या

यह एक सामग्री की संपत्ति है जो दर्शाती है कि सामग्री कितनी दृढ़ता से विद्युत प्रवाह का प्रतिरोध या संचालन करती है। इसे द्वारा निरूपित किया जाता है जिसे rho कहा जाता है। प्रतिरोधकता का सूत्र इस प्रकार दिया गया है,

ρ = (आरए)/एल ⇢ (जहां ‘आर’ प्रतिरोध है, ‘ए’ क्रॉस सेक्शन का क्षेत्र है, ‘एल’ लंबाई है)
ρ = 1/σ (σ चालकता है)

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What is Resistivity?- FAQs

Question 1 What do you mean by resistivity?

Ans. resistivity, electrical resistance of a conductor of unit cross-sectional area and unit length. A characteristic property of each material, resistivity is useful in comparing various materials on the basis of their ability to conduct electric currents. High resistivity designates poor conductors

Question 2 What is resistivity to write its SI unit?

Ans. Resistivity can be defined as the resistance of a conducting material per unit length with unit area of cross section. So it SI unit will be. ρ= RA / l.

Question 3 What is the resistivity of a conductor?

Ans. The resistivity of a conductor is defined as the resistance offered by the material per unit length for unit cross-section. Resistivity is a property of the material and depends on temperature and pressure. The resistivity of conductors is low when compared to the resistivity of the insulators.