in the circuit find the resistance between terminals A and B when switch is open and closed. why both are equal?

To determine the resistance between terminals A and B in a circuit when the switch is open and closed, we need to analyze how the circuit behaves in both scenarios. Let’s break this down step by step.

Understanding the Circuit Configuration

First, it's essential to know the arrangement of components in the circuit. Typically, resistors can be connected in series or parallel, and the presence of a switch can alter the path of current flow. When the switch is open, the circuit is incomplete, while closing the switch allows current to flow through the circuit.

Resistance with the Switch Open

When the switch is open, the current cannot flow through that path. However, if there are other resistors connected in the circuit, we need to consider their arrangement. If terminals A and B are connected through resistors in series or parallel, we can calculate the equivalent resistance using the appropriate formulas:

• Series Resistors: R_total = R1 + R2 + ... + Rn
• Parallel Resistors: 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn

Resistance with the Switch Closed

When the switch is closed, it creates a complete path for current to flow. Depending on the circuit design, closing the switch may either add more resistors in parallel or series with the existing ones. However, if the switch connects directly between terminals A and B, it effectively bypasses any resistors in that path, resulting in a very low resistance (ideally zero if we assume the switch has no resistance).

Why Are Both Resistances Equal?

In some circuits, you might find that the resistance between terminals A and B remains the same whether the switch is open or closed. This can occur in specific configurations where the resistors are arranged such that the overall resistance does not change with the switch's state. For example, if the switch connects two points that do not alter the path of current through the resistors, the equivalent resistance remains constant.

Example Scenario

Consider a circuit with two resistors, R1 and R2, connected in parallel between terminals A and B. If the switch connects a point in the circuit that does not affect the parallel arrangement, the total resistance remains the same regardless of whether the switch is open or closed. This is because the current can still flow through the resistors in parallel, maintaining the same total resistance.

Conclusion

In summary, the resistance between terminals A and B can be equal when the switch is open and closed depending on the circuit configuration. If the switch does not change the effective path of current flow through the resistors, the resistance remains constant. Understanding the arrangement of components and how they interact is key to analyzing such circuits effectively.