Simple series and simple parallel resistor configurations Switch 10 Switch 15 (a

Question

Simple series and simple parallel resistor configurations Switch 10 Switch 15 (a) Circuit 1 (b) Circuit 2. Figure 5.1. Diagrams of (a) series and (b) parallel circuits for study Analyze Circuits 1 and 2 Answer the following questions for both Circuits 1 and 2. Be sure to explain your reasoning and show your calculations in your notes! You can summarize your numerical results in the provided table 1. Which circuit contains the series combination and which the parallel combination? 2. What is the value of current through each resistor? 3. What is the voltage across each resistor? 4. What is the total current flowing through the power supply into the entire circuit? 5. What is the power dissipated (as heat) in each resistor? If any value exceeds 2 W, talk with your TA before proceeding to the next step.

Explanation / Answer

Given

from the given circuits

in circuit 1 , the resistors are connected in series combination and

in circuit 2 , the resistors are connected in parallel combination and

From Ohm's law V = I*R

and in series combination the current through each resistor is same and the potential wiil be different

and in parallel combination the potentaial through each resistor is same and the current wiil be different

so

2) current

series

V = I*R ==> I = V/R

where R is net resistance of the combination

R = R1+R2+R3 = 10+3+15 = 28 ohms

I= 3/28 A = 0.107143 A

in parallel

I = V/R

I1 = V/R1 = 3/12 = 0.25 A

I2 = V/R1 = 3/30 = 0.1 A

I1 = V/R1 = 3/20 = 0.15 A

3) voltage across each resistor

series

V = I*R

V = 0.107143*28 = 3.000004 V = 3 V

so across 10 ohm resistor the voltage is v1 = I*R1 = 0.107143*10 = 1.07143 V

across 3 ohm resistor the voltage is v2 = I*R2 = 0.107143*3 = 0.321429 V

across 15 ohm resistor the voltage is v2 = I*R3 = 0.107143*15 = 1.607145 V

now V = v1+v2+v3 = 1.07143+0.321429+1.607145 = 3.000004 V = 3V

parallel combination

across each resistor the voltage is same which is equal to 3 V

4) total current is  

circuit 1

I1 = V/R

I1 = 3/28 = 0.107143 A

circuit 2

I2 = V/R = 3/(6) = 0.5 A

5) power dissipated is P = V^2/R = i^2*R

series P = i^2*R

P1 = i^2*R1 = 0.107143^2*10 = 0.114796 W

P2 = i^2*R2 = 0.107143^2*3 = 0.0344389 W

P3 = i^2*R3 = 0.107143^2*15 = 0.172194 W

parallel

P = V^2/R

P1 = v^2/R1 = 3^2/12 = 0.75 W

P2 = v^2/R2 = 3^2/30 = 0.3 W

P3 = v^2/R3 = 3^2/20 = 0.45 W

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