Solving Unknown Resistance in Series Circuit

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In summary: This means that the current I1 is the same for the first and second circuit. This also means that the voltage drop on the two known resistors must be equal to the voltage drop on the 7 ohm resistor in the first circuit.In summary, the problem involves finding the unknown resistance R in a series circuit with a 7 ohm resistor, an unknown resistor, a 12 ohm resistor, and a battery. The current through the 7 ohm resistor is the same in both the original and reconfigured circuit. The potential drop must be the same for the 7 ohm resistor in both circuits, leading to the equation 1=1. The solution involves setting the voltage drops on the known resistors equal to
  • #1
syang9
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This problem seems pretty straightforward.. and yet I haven't made any significant progress at all.

"A parallel combination of an 7 resistor and an unknown resistor R is connected in series with a 12 resistor and a battery. This circuit is then disassembled and the three resistors are then connected in series with each other and the same battery. In both arrangements, the current through the 7 resistor is the same. What is the unknown resistance R?"

So I drew the circuit out, and I concluded that for the last statement to be true, the equivalent resistances must be the same (since every resistor in a series circuit feels the same current, by virtue of being in series.) So I wrote

[(1/7) + (1/R)]^-1 + 12 = 7 + 12 + R

Unfortunately this equation is woefully uninformative, as when it is simplified, it yields 1 = 1. Could I have a hint or two from the masters?

Thanks,

Stephen
 
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  • #2
You have to achieve the same potential difference across the 7 ohm resistor in both cases. Get an equation that expresses this voltage in terms of the unknown R for each circuit, and set them equal.
 
  • #3
Why would the potential drop be the same for the 7 ohm resistor in both resistors? In series, wouldn't the voltage drop depend on where the 7 ohm resistor is connected?
 
  • #4
syang9 said:
Why would the potential drop be the same for the 7 ohm resistor in both resistors? In series, wouldn't the voltage drop depend on where the 7 ohm resistor is connected?
The voltage drop on a resistor is RI. Since the problem states that the current is the same in both arrangements, the voltage drps must be equal, as OlderDan said.
 
  • #5
So, here's what I have..

for the first circuit,

V = I1(7Ω) = I2(R); I1 + I2 = Itot

for the second circuit,

V = (7Ω + R)*Itot

so we have I2(R) = (7Ω + R)*Itot; R = Itot (7Ω) / I2. The thing is, Itot is defined in terms of the resistance and the voltage drop.. so I keep getting an identity (i.e., 1=1). So I really don't know what to do.. could you guys help me out?
 
  • #6
syang9 said:
So, here's what I have..

for the first circuit,

V = I1(7Ω) = I2(R); I1 + I2 = Itot

for the second circuit,

V = (7Ω + R)*Itot

so we have I2(R) = (7Ω + R)*Itot; R = Itot (7Ω) / I2. The thing is, Itot is defined in terms of the resistance and the voltage drop.. so I keep getting an identity (i.e., 1=1). So I really don't know what to do.. could you guys help me out?
No, for the second circuit V = 7I1, just as for the first. The difference is that or the second circuit the current I1 passes also through the series connection of the two other resistors.
Since the battery is the same, the voltage drop on the two known resistors must be equal to the voltage drop in the 12 ohm resistor for the first circuit.
 

1. What is the definition of resistance in a series circuit?

Resistance in a series circuit is the measure of the opposition to the flow of electric current. It is caused by the collisions of free electrons with the atoms of the material through which the current is passing. The unit of resistance is ohms (Ω).

2. How do you calculate the total resistance in a series circuit?

The total resistance in a series circuit is equal to the sum of all the individual resistances in the circuit. This can be calculated using the formula Rtotal = R1 + R2 + R3 + ..., where R is the resistance value in ohms.

3. What is the method for solving unknown resistance in a series circuit?

The method for solving unknown resistance in a series circuit is to use Ohm's Law, which states that resistance is equal to the voltage divided by the current. By measuring the voltage and current at different points in the circuit, the unknown resistance can be calculated using the formula R = V/I.

4. What are the common tools used for measuring resistance in a series circuit?

The most common tool used for measuring resistance in a series circuit is a multimeter, which can measure both voltage and current. Other tools include an ohmmeter, which is specifically designed for measuring resistance, and a voltmeter and ammeter, which can also be used to measure voltage and current respectively.

5. What are some potential sources of error when solving unknown resistance in a series circuit?

Some potential sources of error when solving unknown resistance in a series circuit include using inaccurate or faulty measuring tools, incorrect calculations, and fluctuations in the power supply. It is important to double-check all measurements and calculations to minimize these errors.

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