Question

A resistor develops 400 J of thermal energy in 10 s when
a current of 2 A is passed through it. (a) Find its
resistance. (6) If the current is increased to 4 A, what
will be the energy developed in 10 s.​

Answer 1

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GIVEN

•Heat=400J

•time=10s

•current(I)=2A

a)

Use

H=i^2Rt

=>400J=(2A)^2R(10s)

=>400/40=R

=>R=10ohm

hence the value of resistance is 10ohm

Now

b)The thermal energy developed, when the current is 4 A ,is

H=i^2Rt

=>(4)^2(10)(10)

=>16(10)(10)

=>1600J

Answer 2

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Resistance = 10 Ohm.

Heat developed = 1600 Joules.

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GiVeN :

• A resistor produces thermal energy (heat) of 400 J
• Current = 2 A
• Time = 10 seconds

To FiNd :

• Resistance

SoLuTiOn :

We have,

• Heat
• Current
• Time

We need to calculate the resistance.

We have the following formula :-

$\bold{\large{\boxed{\sf{\red{H\:=\:I^2\:\times\:R\:\times\:t}}}}}$

Where,

• H = heat
• I = Current
• R = resistance
• t = time

Block in the values,

$\longrightarrow$$\sf{400\:=\:2^2\:\times\:R\:\times\:10}$

$\longrightarrow$$\sf{400\:=\:4\:\times\:R\:\times\:10}$

$\longrightarrow$$\sf{400\:=\:40\:\times\:R}$

$\longrightarrow$$\sf{\dfrac{400}{40}\:=\:R}$

$\longrightarrow$$\sf{10\:=\:R}$

•°• Resistance = 10 Ohm.

Second part :

GiVeN :

• Current is increased to 4 A
• Resistance = 10 Ohm

To FiNd :

• Energy developed in 10 seconds

SoLuTiOn :

Using the same formula,

$\longrightarrow$$\sf{H\:=\:4^2\:\times\:10\:\times\:10}$

$\longrightarrow$$\sf{H\:=\:16\:=\:100}$

$\longrightarrow$$\sf{H\:=\:1600}$

•°• Heat developed = 1600 Joule.