Question

What is the resistance of an open key? (A) \(\infty\) (B) Can't be determined (C) 0 (D) depends on the other resistance in the circuit

Short answer

The correct answer is (A) \(\infty\). The resistance of an open key is theoretically infinite since it acts as an insulator, preventing the flow of current.

Step-by-step solution

Make sure we understand "open key"

An open key is a switch that is not closed or conducting. In other words, it is a switch that is "open," meaning no current can flow through it. When dealing with resistances in a circuit, an open key has a significant impact on the effective resistance.

Analyze Option A: Infinite resistance

Since no current can flow through an open key, it is acting as an insulator. In theory, the resistance of an insulator is considered to be infinite, i.e., an extremely high value that prevents the flow of current. Therefore, Option A can be the correct answer.

Analyze Option B: Can't be determined

If we already know that an open key is a non-conductive switch with infinite resistance in theory, then this option is incorrect, as we have determined that the resistance of an open key can be estimated.

Analyze Option C: 0 resistance

This option refers to a conductor or a closed key, where current flows freely with no resistance. An open key is the opposite of that; it does not allow the flow of current. Thus, Option C is incorrect.

Analyze Option D: Depends on other resistance in the circuit

The resistance of an open key is independent of the other resistances in the circuit. While the total resistance of a circuit may depend on various factors, the resistance of an open key will always act as an insulator with theoretically infinite resistance. Option D is also incorrect.

Conclusion

Based on the analysis, the resistance of an open key is theoretically infinite, which corresponds to Option (A) \(\infty\). So, the correct answer is (A) \(\infty\).

Key concepts

Open Switch

In electrical circuits, an open switch is a vital component to consider. It can easily stop the flow of electric current. This happens because when a switch is open, the circuit is incomplete. An incomplete circuit does not allow the current to pass through, no matter how strong it is. Think of an open switch like a door that is not fully closed; it prevents anything from passing through from one side to the other. The switch acts like an insulator in this state.

The level of resistance from an open switch is critical because it infinitely increases. This means that theoretically, no current can flow through since it is as if the circuit hits a dead end. Open switches have practical applications in controlling the flow of electricity, like in household light switches, where they determine if the lamp is on or off.

Insulator Resistance

Insulators are materials that block the flow of electric current. They have a very high resistance, which prevents electrons from easily moving through them. In the context of an electrical circuit, an insulator has a substantially higher resistance compared to a conductor. A perfect insulator theoretically has infinite resistance.

This scenario explains the behavior of an open switch. When the switch is open, it acts like an insulator by blocking current passage completely, similar to how rubber or glass would behave. This is why, theoretically, its resistance is considered infinite. Insulators are valuable in circuits because they protect users and components by keeping the current directed through intended paths, minimizing the risk of electrical shocks.

Circuit Theory

Circuit theory is the study of how electrical circuits operate and are designed. It involves understanding various components like resistors, capacitors, and switches. These components interact within a circuit according to specific rules and principles. One primary rule is Ohm's Law, which links voltage, current, and resistance together.

A crucial aspect of circuit theory is understanding how these components, especially switches, impact the circuit's overall resistance. An open switch is a fundamental example. Within circuit theory, it is known to cause infinite resistance, thereby preventing current flow. Understanding how open switches or any component affects the circuit helps engineers design safe and efficient electrical systems. Circuit theory is foundational for diagnosing circuit issues and ensuring a proper flow of electricity.

Current Flow in Circuits

Current flow is the movement of electric charge through a circuit. For current to flow, a complete path from the power source back to itself is needed. This path is often disrupted by open switches, which stop the current flow by breaking the circuit.

In a closed switch scenario, the circuit is complete, and current flows freely with little to no resistance impacting it. When discussing open switches, it's crucial to recognize their role in halting this current flow. They create an infinite resistance point, eliminating any potential for current to continue.

Understanding how current behaves with different circuit configurations ensures that systems operate safely and effectively. It aids in planning how to control and direct current for practical applications, from simple household gadgets to complex industrial machinery.