Finding the current in resistors

In summary, the ideal battery in the circuit has an emf of 6.00 V and is connected to resistors R1 = 99Ω, R2 = R3 = 49.5Ω, and R4 = 75.0Ω. Using the Loop Rule and Junction Rule, the equivalent resistance of the circuit is 18.609Ω. Solving for the current using the equation i = E / (R + r), where E is the emf and R is the equivalent resistance, gives us a current of 0.051 A.
  • #1
Oijl
113
0

Homework Statement


In the figure, R1 = 99 . R2 = R3 = 49.5 . R4 = 75.0 , and the ideal battery has emf script e = 6.00 V.

Re-GLORY.gif


What is i in R1?

Homework Equations


V=IR
Junction Rule
Loop Rule?
i = E / (R+r)


The Attempt at a Solution


The Loop Rule states that for any loop in a circuit, the sum of the voltages across the things in it will be zero. So by combining R2 R3 R4 into Req of resistance 18.609 ohms, I have a loop, so I add the voltages:

E - iR1 - iReq = 0
E = 6 as given in the problem. (Right? Maybe I'm wrong here.)
By the Junction Rule, the current i at R1 and Req would be the same.
So,
6 - i(R1 + Req) = 0
But this just gives me the equivilant resistance for all the resistors, and let's call that plain R.
So I have i = E/R, which is an equation I already had, so I felt good about coming across it via application of the two rules, but when I use this to find the current I don't get the right answer. My numerical answer to the question is 0.51016494 A.

I don't exactly know where I'm going wrong here...

Thank you for looking at this.
 
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  • #2
I get the 18.6 ohms, too. Adding R1 in series, we have 117.6 ohms.
I = V/R = 6/117.6 = .051 A. Looks like you misplaced the decimal point. Quite forgivable at this time of night.
 
  • #3
What is the right answer?
 

Related to Finding the current in resistors

1. How do resistors limit the flow of current?

Resistors are designed to have a specific amount of resistance, which is measured in ohms (Ω). This resistance creates a barrier that hinders the flow of electrons, thus limiting the flow of current in a circuit.

2. How is the current calculated in a resistor?

The current in a resistor can be calculated using Ohm's Law, which states that the current (I) is equal to the voltage (V) divided by the resistance (R). This can be represented by the equation I = V/R.

3. What is the relationship between voltage, resistance, and current in a resistor?

The relationship between voltage, resistance, and current in a resistor can be described by Ohm's Law. As the resistance increases, the current decreases, and vice versa. Similarly, as the voltage increases, the current also increases.

4. How can the current in a resistor be measured?

The current in a resistor can be measured using a multimeter, which is a device that measures voltage, resistance, and current. The multimeter is connected in series with the resistor and the current can be read on the display.

5. Are there any factors that can affect the current in a resistor?

Yes, there are several factors that can affect the current in a resistor. These include the resistance value, voltage, temperature, and the material the resistor is made of. Additionally, the length and thickness of the resistor can also impact the current flow.

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