Resistor Network Analysis

To calculate the voltage between terminals a and b in the given resistor network, we need to analyze the circuit and apply Ohm's law and Kirchhoff's laws.

Step 1: Identify the Resistors in the Circuit
- In the given circuit, there are several resistors connected in a complex network.
- All the resistors have a value of 1 Ω.

Step 2: Analyze the Circuit
- Start by identifying the nodes and branches in the circuit.
- Nodes are the points where three or more circuit elements meet, and branches are the segments between the nodes.
- In this circuit, we can identify two nodes, labeled as a and b, and multiple branches connecting these nodes.

Step 3: Apply Kirchhoff's Laws
- Kirchhoff's laws are fundamental principles used to analyze electrical circuits.
- The first law, known as Kirchhoff's current law (KCL), states that the sum of currents entering a node is equal to the sum of currents leaving the node.
- The second law, known as Kirchhoff's voltage law (KVL), states that the sum of voltages around any closed loop in a circuit is zero.

Step 4: Apply Ohm's Law
- Ohm's law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points.
- Mathematically, Ohm's law is expressed as V = I * R, where V is the voltage, I is the current, and R is the resistance.

Step 5: Solve the Circuit
- Start by applying Kirchhoff's current law at node a.
- Since there is only one current entering node a (1 A), the sum of currents leaving the node must also be 1 A.
- The current splits into three branches at node a, with each branch having a resistance of 1 Ω.
- Therefore, the current through each branch will be 1/3 A.

- Next, apply Kirchhoff's voltage law to find the voltage between terminals a and b.
- Start at node a and follow the loop in the clockwise direction.
- We encounter three resistors, each with a voltage drop of 1 V (according to Ohm's law).
- Finally, we reach node b, where the voltage is the same as at node a.
- Therefore, the voltage between terminals a and b is 3 V.

Conclusion
- The voltage between terminals a and b in the given resistor network is 3 V.
- This result is obtained by analyzing the circuit using Kirchhoff's laws and applying Ohm's law to calculate the current and voltage drops across the resistors.