Q1. A current of 50.0 mA flows in a silver wire of diameter 4.80 mm. Find the strength of the electric field inside the wire.

Background

Topic: Electric Current and Ohm's Law

This question tests your understanding of the relationship between current, electric field, and the properties of a conductor. It involves applying Ohm's law at the microscopic level and using the formula for current density.

Key Terms and Formulas

• Current (): The rate of flow of electric charge, measured in amperes (A).

• Current Density (): , where is the cross-sectional area.

• Ohm's Law (microscopic form): , where is the electric field, is resistivity, and is current density.

• Area of a circle:

Step-by-Step Guidance

1. Convert the current from milliamperes to amperes: .

2. Calculate the radius of the wire in meters: .

3. Find the cross-sectional area of the wire using .

4. Calculate the current density: .

5. Recall that the electric field inside the wire is given by . (You may need to look up the resistivity for silver.)

Try solving on your own before revealing the answer!

Q2a. [Image-based circuit question]

Background

Topic: Circuit Analysis

This question likely involves analyzing a circuit diagram to determine an unknown quantity, such as current, voltage, or resistance. You will need to apply Ohm's Law and possibly rules for series and parallel circuits.

Key Terms and Formulas

• Ohm's Law:

• Series and Parallel Rules for resistors:

  • Series:

  • Parallel:

Step-by-Step Guidance

1. Carefully examine the circuit diagram in the image to identify all components and their arrangement (series or parallel).

2. List all given values (such as voltage, current, or resistance) from the diagram.

3. Apply the appropriate rules for series or parallel circuits to simplify the circuit if needed.

4. Use Ohm's Law to relate the quantities and set up the equation needed to solve for the unknown.

Try solving on your own before revealing the answer!

Q2b. [Image-based circuit question]

Background

Topic: Circuit Analysis (continued)

This question is likely a follow-up to Q2a, possibly with a change in the circuit (e.g., a switch is closed or a component is added/removed). The approach will be similar but pay attention to what has changed.

Key Terms and Formulas

• Ohm's Law:

• Series and Parallel Rules for resistors (as above)

Step-by-Step Guidance

1. Identify what has changed in the circuit compared to Q2a (e.g., a switch position, added/removed resistor).

2. Redraw or mentally adjust the circuit to reflect the change.

3. Recalculate the equivalent resistance if necessary.

4. Apply Ohm's Law and the rules for series/parallel circuits to set up the equation for the unknown.

Try solving on your own before revealing the answer!

Q3a. Switch S is open: find the value of resistance .

Background

Topic: Circuit Analysis with Switches

This question involves analyzing a circuit with a switch in the open position. You are given the current (45.0 mA) and voltage (9.00 V) and asked to find the resistance .

Key Terms and Formulas

• Ohm's Law:

Step-by-Step Guidance

1. Convert the current from milliamperes to amperes: .

2. Write Ohm's Law for the circuit: .

3. Rearrange to solve for : .

4. Plug in the given values for and .

Try solving on your own before revealing the answer!

Q3b. Switch S is closed: find the value of the unknown resistance .

Background

Topic: Circuit Analysis with Switches (continued)

Now the switch is closed, and the current increases to 62.5 mA with the same voltage (9.00 V). You are to find the value of the unknown resistance .

Key Terms and Formulas

• Ohm's Law:

• Rules for combining resistors (series/parallel) if applicable

Step-by-Step Guidance

1. Convert the current from milliamperes to amperes: .

2. Write Ohm's Law for the new circuit: .

3. Express in terms of and (depending on their arrangement in the circuit).

4. Plug in the values for and and solve for .

Try solving on your own before revealing the answer!

Q4a. Find the current flowing through resistance .

Background

Topic: Current Division in Circuits

This question asks you to find the current through a specific resistor, , in a circuit. You will need to use the rules for series and parallel circuits and possibly the current divider rule.

Key Terms and Formulas

• Ohm's Law:

• Current Divider Rule (for parallel branches): (for two resistors in parallel)

Step-by-Step Guidance

1. Identify the arrangement of in the circuit (series or parallel).

2. Calculate the total resistance if needed.

3. Find the total current in the circuit using Ohm's Law.

4. Apply the current divider rule if is in parallel, or use Ohm's Law directly if in series.

Try solving on your own before revealing the answer!

Q4b. Find the current flowing through resistance .

Background

Topic: Current Division in Circuits (continued)

This question is similar to Q4a but for a different resistor, . The approach will be the same: analyze the circuit, determine the arrangement, and apply the appropriate rules.

Key Terms and Formulas

• Ohm's Law:

• Current Divider Rule (if applicable)

Step-by-Step Guidance

1. Identify the arrangement of in the circuit (series or parallel).

2. Calculate the total resistance if needed.

3. Find the total current in the circuit using Ohm's Law.

4. Apply the current divider rule if is in parallel, or use Ohm's Law directly if in series.

Try solving on your own before revealing the answer!