COLLEGE PHYSICS (OER)
COLLEGE PHYSICS (OER)
1st Edition
ISBN: 9781947172012
Author: DIRKS
Publisher: OpenStax
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Chapter 21, Problem 5TP
To determine

(a)

The resistors with maximum current.

Expert Solution
Check Mark

Answer to Problem 5TP

  R4=4Ω has the maximum current in the circuit.

Explanation of Solution

Given:

Parallel combination of two 20Ω and one 10Ω resistors is connected in series with a 4Ω resistor.

Source voltage = 36V.

Calculations:

With the given information, following circuit diagram can be drawn:

  COLLEGE PHYSICS (OER), Chapter 21, Problem 5TP , additional homework tip  1

Here, the resistors R1=R2=20Ω,R3=10Ω, and R4=4Ω .The voltage source is 36V.

The resistor which provides the maximum current is R4=4Ω ,because the current that goes through R4 is the total current in the circuit and that current is equally distributed in the three branches of resistors.

Conclusion:

Thus, R4 is the resistor which provide the maximum current.

To determine

(b)

The resistor with maximum voltage drop.

Expert Solution
Check Mark

Answer to Problem 5TP

Each of the resistor connected in parallel have the maximum voltage drop.

Explanation of Solution

Given:

Parallel combination of two 20Ω and one 10Ω resistors is connected in series with a 4Ω resistor.

Source voltage = 36V.

Calculations:

With the given information, following circuit diagram can be drawn:

  COLLEGE PHYSICS (OER), Chapter 21, Problem 5TP , additional homework tip  2

Here, the resistors R1=R2=20Ω,R3=10Ω, and R4=4Ω .The voltage source is 36V.

To find the voltage drop in the above circuit, compare the voltage across of R1,R2,R3 with a voltage across R4.

So, for finding the voltage drop, find the equivalent resistance separately as follows:

  R1,R2, and R3  are in parallel. Their equivalent resistance can be calculated as follows:

  1R eq=1R1+1R2+1R3                           {Formula to find the equivalent resistance}1R eq=120+120+110                              {where,R1=R2=20Ω,R3=10Ω}1R eq=1+1+2201R eq=1+1+2201R eq=420Req=5Ω

Conclusion:

Thus, the equivalent resistance of 5Ω is greater than the R4. So, each of the resistor connected in parallel will have the maximum voltage drop.

To determine

(c)

The power dissipated in each of the resistor and total power dissipated in all resistor.

Expert Solution
Check Mark

Answer to Problem 5TP

20 W in each 20Ω resistor, 40 W in 10Ω resistor. Total = 144 W.

Output power source = 144 W.

Yes, they are equal as per law of conservation of energy.

Explanation of Solution

Given:

Parallel combination of two 20Ω and one 10Ω resistors is connected in series with a 4Ω resistor.

Source voltage = 36V.

Calculations:

With the given information, following circuit diagram can be drawn:

  COLLEGE PHYSICS (OER), Chapter 21, Problem 5TP , additional homework tip  3

Here, the resistors R1=R2=20Ω,R3=10Ω, and R4=4Ω.

The voltage source is 36V.

To find the power dissipated in each of the resistor and the total power dissipated in each of the resistor, follow some steps one by one as below:

  1. Find the equivalent resistance and then find the total current.
  2.   1R=1R1+1R2+1R3                           {Formula to find the equivalent resistance}1R=120+120+110                              {where,R1=R2=20Ω,R3=10Ω}1R=1+1+2201R=1+1+2201R=420R=5ΩParallel combination of the circuit with series resistance.Req=R+R4=5Ω+4Ω=9Ω              {,R4=4Ω}Total current:I=VR=369=4A                                 {Voltage source(V)=36 ,R=9}

      Step 2: Voltage across parallel combination of resistance (R1,R2,R3) are:

  3. Voltage across parallel combination of resistance.
  4.   V=I×RV=4×5                                               {where,I=4 and R=5}V=20 V

  5. Calculate the power dissipated in each resistor are:
  6.   P1=V2R= (20)220=40020=20 wattP2=V2R= (20)220=40020=20 wattP3=V2R= (20)210=40010=40 wattPower dissipated across the resistance (R4) are: P 4 = I 2 R= (4) 2 4=64 watt

  7. Total power dissipated in all the resistor.
  8.   P=P1+P2+P3+P4P=20+20+40+64P=144 watt

  9. Find the total power output of the source as follows:
  10.   Total power output source(P)=IV                           {Substitute the value of I=4A and V=36V}                                                =4×36                                                =144 W

Conclusion:

The power dissipated of all the resistor and the total power output source are equal by the law of conservation of energy.

To determine

(e)

The values of all the resistors and the source voltage are doubled.

Expert Solution
Check Mark

Answer to Problem 5TP

No effect.

Explanation of Solution

Given:

Parallel combination of two 20Ω and one 10Ω resistors is connected in series with a 4Ω resistor.

Source voltage = 36V.

Calculations:

With the given information, following circuit diagram can be drawn:

  COLLEGE PHYSICS (OER), Chapter 21, Problem 5TP , additional homework tip  4

Here, the resistors R1=R2=20Ω,R3=10Ω, and R4=4Ω .The voltage source is 36V.

If the values of all the resistors and the source voltage are doubled, then there would be no effect on the current.

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