I am confused when it comes to this AC circuit problem. It is part e. The back o

Question

I am confused when it comes to this AC circuit problem. It is part e. The back of the book shows that V_R3 = 100 V. But as you see from my calculations, I get V_R1 = 20 V and
V_R2 = 100 V. So shouldn't V_R3 = 0 V because the original voltage source for this AC circuit is 120 V, yet the book says V_R3 = 100 V.

I am used to DC where you add up the voltages on each resistor and see if it equals the total voltage source. Hope you guys can help because we just started this stuff this week.

Q: Draw the diagram of a three resistor series parallel circuit having a 10-k? resistor (labeled R_1) in series with the source, and two 100-k? resistor (labeled R_2 and R_3) in parallel with each other and in series with R_1. Assume a 120-V ac source. Calculate the following parameters and appropriate label them on the diagram:
a.) V_R1
b.) I_R1
c.) P_R1
d.) I_R2
e.) V_R3
f.) ? between V applied and I total
__________________________________________________ _________________________
My Calculation:
Picture of Circuit:
http://img87.imageshack.us/f/circuith.png/

R_equ1 = 1/((1/R_2)+(1/R_3)) = 1/((1/100 k?)+(1/100 k?)) = 50 k?
R_T = R_1 + R_equ1 = 10 k? + 50 k? = 60 k?
V_T = I_T * R_T
I_T = V_T / R_T = 120 / 60 k? = 2 mA

a.)
V_R1 = I_T * R_1= 2 mA * 10 k? = 20 V
b.)
V_R1 = I_R1 * R_1
I_R1 = V_R1/ R_1 = 20 V / 10 k? = 2 mA
c.)
P = V_R1² / R_1 = (20 V)² / 10 k? = 40 mW
d.)
V_T = V_R1+ V_R2
V_R2= V_T - V_R1= 120 V – 20 V = 100 V
V_R2= I_R2* R_2
I_R2 = V_R2/ R_2 = 100 V / 100 k? = 1 mA
e.)
V_T = V_R1 + V_R2 + V_R3
V_R3= V_T - V_R1- V_R2= 120 V – 20 V – 100 V
= 0V

Explanation / Answer

Soln :::

Part .E.))

Req_1=50 K ,R1=10K

Itotal=2mA .

Vlotage Across Req_1= 50K * 2mA =100V.

Since Req_1 consists of two parallel resistance AND we know that Parallel resistance have Same potential difference in the Circuit .

Voltage Across R2 & R3 is same i.e 100V .

Therefore , VR2 =100V . ,....Answer

Part F.) Total Equivalent Resistance b/w Voltage Applaid & total Current is = Vapplaid /Itotal = 120V/2mA =60 K

Total Equivalent Resitance = 60K ....Answer

Thanking You ...

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