Voltage, Current, and Resistance Calculations

[a1234]

Homework Statement

I'm asked to find the voltage, current, and resistance through each resistor in the given circuit.

Homework Equations

Req for parallel = 1/R1 + 1/R2 + ...
Req for series = R1 + R2 + ...

The Attempt at a Solution

First, I want to find the total resistance in the circuit.
Since R3 and R5 are in series, is R35 = 18 ohms?
Then R4 and R35 would be in parallel, so 1/9 + 1/18 = 1/Req
Req = 6 ohms

6 + 9 + 2.5 = 17.5 ohms
Is this the total resistance in the circuit?

 

[haruspex]

Homework Statement

I'm asked to find the voltage, current, and resistance through each resistor in the given circuit.

Homework Equations

Req for parallel = 1/R1 + 1/R2 + ...
Req for series = R1 + R2 + ...

The Attempt at a Solution

First, I want to find the total resistance in the circuit.
Since R3 and R5 are in series, is R35 = 18 ohms?
Then R4 and R35 would be in parallel, so 1/9 + 1/18 = 1/Req
Req = 6 ohms

6 + 9 + 2.5 = 17.5 ohms
Is this the total resistance in the circuit?

Yes, that is all correct.

 

[a1234]

Here are the calculations I have so far:
R1: 0.69 amps, 6.17 volts
R2: 0.69 amps, 1.17 volts
R4: 1.33 amps, 12 volts

For R3 and R5, am I supposed to consider them to be in series with the battery, or in parallel?

 

[haruspex]

Here are the calculations I have so far:
R1: 0.69 amps, 6.17 volts
R2: 0.69 amps, 1.17 volts
R4: 1.33 amps, 12 volts

For R3 and R5, am I supposed to consider them to be in series with the battery, or in parallel?

I agree with the current through R1 and R2 (but closer to 0.68?), and the voltage across R1.
Your voltage across R2 looks like a typo (transposed digits).
There is no way that R4 can have a larger current than R1 and R2.

 

[a1234]

For R2, the voltage is 0.69 * 2.5 = 1.725. I don't know how I ended up with 1.17.
For R4, I thought it was in parallel and did 12 = 9 * I to get I = 1.33 amps.

 

[haruspex]

For R2, the voltage is 0.69 * 2.5 = 1.725. I don't know how I ended up with 1.17.
For R4, I thought it was in parallel and did 12 = 9 * I to get I = 1.33 amps.

The current that goes through R1 gets split, some going through R4, the rest through R5 and R3.

 

[a1234]

Would the voltage going through R4 be different from 12 V?

 

[haruspex]

Would the voltage going through R4 be different from 12 V?

The voltage across R4 will be less than 12V. What is the voltage drop across R1?

 

[a1234]

12/17.5 = 0.69
0.69 * 9 = 6.17 volts

 

[haruspex]

12/17.5 = 0.69
0.69 * 9 = 6.17 volts

Right, and you also calculated the drop across R2. So what is the drop across R4?

 

[a1234]

Would we work backwards to get 12 - 6.17 - 1.17 = 4.66, and divide that by 3?

 

[haruspex]

Would we work backwards to get 12 - 6.17 - 1.17

1.71

and divide that by 3?

why 3?

 

[a1234]

The voltage drop across R4 is 12 - 6.17 - 1.71 = 4.12 V.

 

[haruspex]

The voltage drop across R4 is 12 - 6.17 - 1.71 = 4.12 V.

Right, so what is the current through it?