# Applying Kirchoff's rule

• Petey_Smalls
In summary, the circuit shown in fig. 27-29 has an input voltage of 35.0 V, with resistances of 6.00 Ω and 1.00 Ω. To find the current in resistor R, we use the sum of currents at a junction and find that it is 2 A. To solve for the resistance of R, we can use Kirchoff's voltage law and the fact that the sum of voltage drops around a loop in a circuit is zero. By setting one point as the reference for zero voltage, we can calculate the voltage difference across each resistor using V=IR and the voltage of each battery. This will allow us to solve for the unknown voltage ε and then use V

## Homework Statement

In the circuit shown in fig. 27-29, ε1 = 35.0, R1 = 6.00 , and R2 = 1.00 .

a. Find the current in resistor R.
b. Find the resistance R
c. Find the unknown emf. ε.
d. If the circuit is broken at point x, what is the magnitude of the current in the 35.0 V battery?

sigmaI=0
sigmaV=0

## The Attempt at a Solution

I got that the current is 2 A, based on the sum of currents at a junction. But I can't solve for the resistance of R. I tried V=IR, with I=2, but I guess I was using the wrong V, since 6 is not the answer to b. Then I figured that I needed b to solve for c, so I came here looking for some help. Thanks in advance.

You can (and pretty much have to) use V = IR. As you already figured out, you need to find the correct value of V. Think how you might use Kirchoff's voltage law (that the sum of voltage drops around a loop in a circuit is zero) to do this. Which loop would you pick?

I'd do it by saying that one point in the circuit is at 'zero' voltage (it doesn't matter where you pick) and work out what the voltage of all the other points relative to this (you can use V = IR across resistors - remembering that the V in this equation is the _difference_ in voltage across the resistor) and of course the voltage difference across each battery is the voltage of the battery.

You should be able to work out a voltage for either side of that resistor like that, _then_ you can use V=IR.

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## 1. What is Kirchoff's rule and why is it important in science?

Kirchoff's rule, also known as Kirchoff's circuit laws, are two fundamental principles in electrical circuit analysis. The first law, or Kirchoff's current law, states that the sum of currents entering a node in a circuit must equal the sum of currents leaving that node. The second law, or Kirchoff's voltage law, states that the sum of voltage drops in a closed loop must equal the sum of voltage sources in that loop. These rules are important for understanding and analyzing complex electrical circuits.

## 2. How is Kirchoff's rule applied in circuit analysis?

Kirchoff's rule is applied by using the first law to determine the currents in different branches of a circuit, and then using the second law to calculate the voltage drops across different components. This allows for the determination of important parameters such as voltage, current, and resistance in a circuit.

## 3. Can Kirchoff's rule be used in all types of circuits?

Yes, Kirchoff's rule can be applied to any type of circuit, whether it is a simple series or parallel circuit, or a more complex circuit with multiple loops and branches. The principles of Kirchoff's rule remain the same regardless of the complexity of the circuit.

## 4. What are the limitations of Kirchoff's rule?

Kirchoff's rule assumes that the circuit is in a steady state, meaning that the currents and voltage in the circuit are constant and do not change over time. It also assumes that the circuit is linear, meaning that the components in the circuit follow Ohm's law. Additionally, Kirchoff's rule does not account for the effects of capacitance and inductance in a circuit.

## 5. Are there any real-world applications of Kirchoff's rule?

Yes, Kirchoff's rule is used in a variety of real-world applications, such as in the design and analysis of electrical circuits in electronics and power systems. It is also used in other fields such as telecommunications, where it is used to analyze and design communication networks. Kirchoff's rule is a fundamental principle in the study of electrical circuits and is applied in many different industries and technologies.