Question

Derive an expression for the heat produced in a conductor of resistance R when a current flow through

if for time t.

Two identical resistors of resistance R are connected in series with a battery of potential difference V

for time t. the resistors are then connected in parallel with the same battery for the same time t.

Compare the heat produced in the two cases Please tell now​

Answer 1

Derivaƭon: For work done, , on moving

W

a net charge, , the potential difference is

defined as,

Q

V

= QW

⇒ W = VQ

Let be the time it takes to move the net charge

t

. Multiplying and dividing the R.H.S. by , weget,

Q

W = V ×× t t

= VIt

Q

where is the current, , by definition.

[ mark] t 1

I

Since this work is converted into heat energy, we can write,

W = H = VIt

=(IR)× It

2

H = IRt

where is the resistance in the circuit and

R

Ohm's law () is applied in the second

step.

[ mark]

V = IR

1

Second part: We obtained, .

W = H = VIt

I = RV

Writing from Ohm's law, we get,H = V ×× t

V 2 = t R

H ∝ R1

[ mark]

1

If two equal resistances, each, are connected

R

in series, the equivalent resistance,

R =

S R + R =2R.

When connected in parallel, the equivalent resistance, , is found as,

1 RP

RP

1 =+ R R

RP = 2R

[ mark]

1

1

Let the heat produced in the series combination be , and the parallel

HS

combination be . We have,HS

1/RS

HP = 1/RP

RP = RS

R =× 2R 2

1 P HS = H 4

HP =4HS

1

Therefore, the heat produced in the parallel combination is four times that of the series combination. [ mark]

Explanation:

Answer 2

Explanation:

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