Current, Resistance, and Boundary Conditions Quiz Quiz

Explore essential concepts of electric current, resistance, and boundary conditions in circuits with this focused quiz. Assess your understanding of Ohm's Law, resistor arrangements, and how electrical boundaries affect circuit behavior.

1. Calculating Current Using Ohm’s Law

   If a resistor of 10 ohms is connected across a 20-volt battery, what is the current flowing through the resistor according to Ohm's Law?

   1. 30 amperes
   2. 2 amperes
   3. 20 amperes
   4. 0.5 amperes

   Explanation: Ohm's Law states that current equals voltage divided by resistance, so 20 volts divided by 10 ohms gives 2 amperes. Option 0.5 amperes results from incorrectly dividing 10 by 20. 30 amperes and 20 amperes are unrealistic for this setup and suggest misunderstanding of Ohm’s Law. Only 2 amperes matches both the numerical calculation and the units.

2. Understanding Series vs. Parallel Resistance

   A circuit has two resistors, each 4 ohms, first connected in series and then in parallel. Which configuration results in a lower total resistance, and what is the total resistance for that configuration?

   1. Series, 2 ohms
   2. Parallel, 2 ohms
   3. Series, 8 ohms
   4. Parallel, 4 ohms

   Explanation: In parallel, the total resistance is the product over the sum: (4x4)/(4+4)=16/8=2 ohms, which is lower than the 8 ohms of a series setup. Series, 8 ohms is the correct series calculation, but the question asks for the lowest resistance. Parallel, 4 ohms and Series, 2 ohms do not result from the given resistor values.

3. Boundary Conditions at the Interface of Two Materials

   At the interface between a conductor and an insulator in a steady electric circuit, what happens to the current density at the boundary?

   1. It becomes negative in the insulator
   2. It drops to zero in the insulator
   3. It remains the same in both materials
   4. It increases in the insulator

   Explanation: Current cannot flow in an ideal insulator, so the current density drops to zero at the boundary. It cannot remain the same or increase in the insulator because an insulator does not conduct. The concept of 'negative current density' in the insulator is incorrect in this context, as current simply ceases.

4. Effect of Increasing Wire Length on Resistance

   If you double the length of a uniform wire while keeping its cross-sectional area and material the same, what happens to the wire’s resistance?

   1. Resistance remains unchanged
   2. Resistance halves
   3. Resistance doubles
   4. Resistance quadruples

   Explanation: Resistance is directly proportional to the length of a wire, so doubling the length doubles the resistance. Halving resistance would require the length to be halved, not doubled. Unchanged resistance occurs if the length and area are constant. Quadrupling resistance would happen if both length doubled and area halved, which is not the case here.

5. Current Flow at a Junction (Kirchhoff’s Law)

   In an electrical circuit, three wires meet at a junction: 2 amperes flow in from the first wire, 3 amperes in from the second, and 4 amperes flow out via the third. According to Kirchhoff’s current law, what must happen at the junction?

   1. The junction accumulates excess charge
   2. 1 ampere must flow out through another wire
   3. No current can flow through the junction
   4. All current must flow into the junction only

   Explanation: Kirchhoff’s current law states that total current in equals total current out, so (2A + 3A) in and 4A out leaves 1A unaccounted for, requiring an additional 1A to flow out for balance. All current entering is incorrect as current must leave as well. Accumulation of charge at a junction does not occur in steady-state circuits. Stating that no current can flow through the junction contradicts the initial scenario.