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  • (a) Consider circuit in Figure. How much energy is absorbed by electrons from the initial state of no current (ignore thermal motion) to the state of drift velocity?

(a) Consider the circuit in Figure. How much energy is absorbed by electrons from the initial state of no current (ignore thermal motion) to the state of drift velocity?

(b) Electrons give up energy at the rate of RI_2  per second to the thermal energy. What time scale would one associate with energy in problem (a)? n = no of electron/volume = 10^{29}/m^3, length of circuit = 10 cm, cross-section = A = (1mm)^2

Answers (1)

1)

Step 1: Find the current in the circuit.

Formula used: V=IR

Given, the voltage of the battery, V=6 V

And resistance, R=6 Ω

So current in the circuit,

I = \frac{V}{R} = \frac{6}{6} = 1A

Step 2: Find the drift velocity of the electrons.

Formula used: I=neAvd

Given,

n= no of electron/volume =1029/m3

Area of cross-section =A=(1 mm)2

So, the drift velocity of the electron

v_d= \frac{I}{neA} \\ \\ v_d= \frac{1}{10^{29} \times 1.6 \times 10^{-19} \times 10^{-6}} m/s


Step 3: Find energy absorbed by the electrons.

Given, the length of the circuit, l=10 cm

Energy absorbed by the electron is the kinetic energy gained due to drift velocity.

E = \frac{1}{2} m v_{d}^{2}

Energy absorbed by all the electrons

E = \frac{1}{2} m v_{d}^{2}(nAI)

E = \frac{1}{2} (9.1 \times 10^{-31})(\frac{1}{10^{29} \times 1.6 \times 10^{-19} \times 10^{-6}})^{2} (10^{29} \times 10^{-6} \times 10 \times 10^{-2})

E=1.78×10−17 J

Final answer:1.78×10−17 J

2)

Step 1: Find energy given up by electron per second.

Formula used: P=I2R

Given, the voltage of the battery, V=6 V

And resistance R=6 Ω

So current in the circuit, 

I = \frac{V}{R} = \frac{6}{6} = 1A

So, power loss, P=I2R

P=(1)2(6)=6 W

Step 2: Find the time associated.

Formula used:

P=\frac{E}{t}

Power loss is energy dissipated per second.

P=\frac{E}{t}
t=\frac{E}{P}= \ \frac{1.78 \times 10^{-17} \ J}{6J/s} = 3 \times 10^{-18}s

Final answer:3×10−18s

Posted by

infoexpert24

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