Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
Question
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Chapter 38, Problem 54P

(a)

To determine

The resistance for small reverse-bias voltages.

(a)

Expert Solution
Check Mark

Answer to Problem 54P

The resistance for small reverse-bias voltages is 25 .

Explanation of Solution

Given:

The saturation current is I0= 1.0 nA .

The value of kT=0.025eV .

Formula used:

The expression for Ohm’s Law is

  R=VbI

Here, R is the resistance, Vb is the voltage and I is the current in the circuit.

The expression for current in semiconductor is,

  I=I0(ee V b/kT1)

Calculation:

For small reverse-bias voltages i.e eVb<<kT

  ee V b/kT11+eVbkT1=eVbkT

The expression for current in semiconductor is then reduced to,

  I=I0(e e V b / kT 1)=I0eVbkT

The expression for Ohm’s Law is then derived as,

  R=VbI0 e V b kT=kTeI0

The resistance is further calculated as,

  R=kTeI0=( 0.025eV)( 1.6× 10 19 J/ eV )( 1.6× 10 19 C)( 1.0× 10 9 A)=25

Conclusion:

Therefore, the resistance for small reverse-bias voltages is 25 .

(b)

To determine

The resistance for reverse bias of 0.50 V

(b)

Expert Solution
Check Mark

Answer to Problem 54P

The resistance for reverse bias of 0.50 V is 5.0×108Ω .

Explanation of Solution

Formula used:

The resistance for reverse bias of 0.50 V is,

  R=VbI0(e e V b / kT 1)

Calculation:

Evaluating the term eVbkT for Vb=0.50V

  eVbkT=( 1.6× 10 19 C)( 0.50V)( 0.025eV)( 1.6× 10 19 J/ eV )=19.8

The resistance for reverse bias of 0.50 V is calculated as,

  R=VbI0( e e V b / kT 1)=0.50V( 1.0× 10 9 A)( e 19.8 1)=5.0×108Ω

Conclusion:

Therefore, the resistance for reverse bias of 0.50 V is 5.0×108Ω .

(c)

To determine

The resistance for a 0.50V forward bias and the corresponding current.

(c)

Expert Solution
Check Mark

Answer to Problem 54P

The resistance for forward bias of 0.50 V is 1.3Ω and corresponding current is 0.38A .

Explanation of Solution

Formula used:

The resistance for forward bias of 0.50 V is,

  R=VbI0(e e V b / kT 1)

Calculation:

Evaluating the term eVbkT for Vb=0.50V

  eVbkT=( 1.6× 10 19 C)( 0.50V)( 0.025eV)( 1.6× 10 19 J/ eV )=19.8

The resistance for reverse bias of 0.50 V is calculated as,

  R=VbI0( e e V b / kT 1)=0.50V( 1.0× 10 9 A)( e 19.8 1)=1.3Ω

Current is calculated from Ohm’s Law,

  I=VR=0.50V1.3Ω=0.38A

Conclusion:

Therefore, the resistance for forward bias of 0.50 V is 1.3Ω and corresponding current is 0.38A .

(d)

To determine

The AC resistance for a 0.50V forward bias voltage.

(d)

Expert Solution
Check Mark

Answer to Problem 54P

The AC resistance for forward bias of 0.50 V is 63 .

Explanation of Solution

Formula used:

The resistance for forward bias of 0.50 V is,

  R=VbI0(e e V b / kT 1)

The AC resistance is expressed as,

  Rac=dVdI=( dI dV)1

Calculation:

The AC resistance is calculated as,

  Rac={d dV( I 0 ( e e V b / kT 1 ))}1={ e I 0 kTe e V b / kT }1=kTeI0ee V b/kT=(25)e19.8

The calculation is further simplified as

  Rac=25×106Ω×2.5×109Ω=63

Conclusion:

Therefore, the AC resistance for forward bias of 0.50 V is 63 .

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