Question

Physics Class IX

Q1) How is the current flowing in a conductor changed if the resistance of the conductor is doubled keeping the potential difference across it the same?

Q2) How is the resistance of the wire affected if its:
(a) length is doubled
(b) radius is doubled

Q3) How will the resistance of the filament of the bulb will decrease, increase or remains same. Explain.
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Thanks!
#BeBrainly :)​

Answer 1

Topic

Electricity

Formula to be Used

I = V / R

R = pl / A

where

I = Current in Conductor

V = Potential difference across Conductor

R = Resistance of Conductor

p = Resistivity of Resistor

l = length of Resistor

A = Cross - sectional Area of Resistor

Solution

1) It is given that Resistance of Conductor is doubled keeping potential difference same across it.

Current before performing steps

I = V / R

Current after performing steps

I' = V / 2R

Change factor = I' / I

( V / 2R ) / ( V / R )

1 / 2

I' / I = 1 / 2

I' = I / 2

So, current gets halved.

2 ) a) It is given that length of Resistor is doubled.

Resistance before performing steps,

R = pl / A

Resistance after performing steps,

R' = p( 2l ) / A

Change factor = R' / R

( p( 2l ) / A ) / ( pl / A )

2

R' / R = 2

R' = 2R

So, resistance gets doubled.

b) It is given that radius of Resistor is doubled.

Resistor is in form of cylindrical wire,

Area of Cross section of cylindrical wire that is circle is πr².

Resistance before performing steps,

R = pl / πr²

Resistance after performing steps,

R' = pl / π(2r)²

R' = pl / 4πr²

Change factor : R' / R

( pl / 4πr² ) / ( pl / πr² )

1 / 4

R' / R = 1 / 4

R' = R / 4

So, resistance gets one - fourth.

3) Resistance of filament of bulb will increase when it is in use because the filament of bulb gets heated which results in increase of Temperature and increase in Temperature results in increase of Resistance of a conductor. It can be also noted that due to high temperature energy of ions present in resistor increases which leads to fast movement of ions which decreases relaxation time and decrease in relaxation time leads to increase in Resistance.

Answer 2

Answer

• 1Using Ohm's law, for constant potential difference, we may write:

.

$I∝R1$

• So, The current flowing in a conductor is halved if the resistance of the conductor is doubled keeping the potential difference across it the same.
• 2 Resistance of a wire is directly proportional to the length of a wire; so if the length is doubled, resistance is also doubled
• Thus, if radius is doubled, area increases four times and hence the resistance becomes one-fourth.

• 3 The temperature of the filament increases when it glows. So, when the temperature of the bulb filament increases, ions in it vibrate violently. As a result, the number of collisions increases and hence the resistance increases.