# Expert Answer resistors and a battery - Expert Answer

1) Expert Answer resistors and a battery with a 9 V EMF which has a 1 O internal resistance. Determine

a) The current in each resistor. It should be clear (when I read your paper) as to which current goes with each resistor.

b) The terminal voltage of the battery,

c) The total power input using eI, and the power output for each resistor individually, including the internal resistance, by using IR (I is the current in the individual resistor).

Sum these individual outputs and show that the power output is equal to the power input.

2) A, B and C are identical light bulbs (see diagram below/next page). The internal resistance of the battery is small relative to the resistance's of the bulbs, but its effects are still noticeable.

a) Assume that the resistance of each bulb is R. Without substituting numerical values derive a formula for the equivalent resistance of the external resistors (the bulbs) for each case: switch open and switch closed. How does closing the switch affect the equivalent resistance of the circuit?

b) How does closing the switch affect the amount of current in the battery? How does closing the switch affect the terminal voltage of the battery? Explain how you know.

c) Discuss what happens to the brightness of bulb A when the switch is closed. How is your answer here related to the current in the battery?

d) With the switch closed, bulb B is unscrewed from its socket. How does this affect the brightness of bulb A? How can this behavior be explained?

Explain your reasoning for all answers. You are encouraged to construct actual

circuits, for instance in the PRL, but you must provide an underlying theory that explains the behavior of the circuits.

3) In the circuit below a battery with a 9 V emf and a 2 O internal resistance is connected to two resistors and a switch that connects points a and b. The + and - represent the poles of the battery.

a) With the switch open determine the current in the battery and the current in each resistor.

b) Determine the terminal voltage of the battery.

c) Now the switch is closed. To make the math easier assume that the resistance between =0.1 O. Determine the terminal voltage

across the battery and the current in the 20 O resistor.

d) Compare the power output of the 20 O resistor with the switch open to the output points a and b in the circuit is small but finite: R ab when the switch is closed. If this resistor were a light bulb how would closing the switch affect its behavior?

4) In the circuit below the 0.5 O and 0.9 O resistors represent the internal resistance's of the two batteries. The other four resistors are external.

a) Apply Kirchoff’s rules to the circuit and generate enough equations to determine the current in each element of the circuit. Label the unknown currents (separately drawn diagram of the circuit on solution sheet) and indicate the loops and junctions that relate to the equations. Solve the equations for the unknown currents.

b) Determine the terminal voltage of the battery with the 2.0 V EMF.

Note: We will discuss matrix based methods in class to solve systems of linear equations such as those generated for this circuit. You may use your calculators to implement these methods.

a) The current in each resistor. It should be clear (when I read your paper) as to which current goes with each resistor.

b) The terminal voltage of the battery,

c) The total power input using eI, and the power output for each resistor individually, including the internal resistance, by using IR (I is the current in the individual resistor).

Sum these individual outputs and show that the power output is equal to the power input.

2) A, B and C are identical light bulbs (see diagram below/next page). The internal resistance of the battery is small relative to the resistance's of the bulbs, but its effects are still noticeable.

a) Assume that the resistance of each bulb is R. Without substituting numerical values derive a formula for the equivalent resistance of the external resistors (the bulbs) for each case: switch open and switch closed. How does closing the switch affect the equivalent resistance of the circuit?

b) How does closing the switch affect the amount of current in the battery? How does closing the switch affect the terminal voltage of the battery? Explain how you know.

c) Discuss what happens to the brightness of bulb A when the switch is closed. How is your answer here related to the current in the battery?

d) With the switch closed, bulb B is unscrewed from its socket. How does this affect the brightness of bulb A? How can this behavior be explained?

Explain your reasoning for all answers. You are encouraged to construct actual

circuits, for instance in the PRL, but you must provide an underlying theory that explains the behavior of the circuits.

3) In the circuit below a battery with a 9 V emf and a 2 O internal resistance is connected to two resistors and a switch that connects points a and b. The + and - represent the poles of the battery.

a) With the switch open determine the current in the battery and the current in each resistor.

b) Determine the terminal voltage of the battery.

c) Now the switch is closed. To make the math easier assume that the resistance between =0.1 O. Determine the terminal voltage

across the battery and the current in the 20 O resistor.

d) Compare the power output of the 20 O resistor with the switch open to the output points a and b in the circuit is small but finite: R ab when the switch is closed. If this resistor were a light bulb how would closing the switch affect its behavior?

4) In the circuit below the 0.5 O and 0.9 O resistors represent the internal resistance's of the two batteries. The other four resistors are external.

a) Apply Kirchoff’s rules to the circuit and generate enough equations to determine the current in each element of the circuit. Label the unknown currents (separately drawn diagram of the circuit on solution sheet) and indicate the loops and junctions that relate to the equations. Solve the equations for the unknown currents.

b) Determine the terminal voltage of the battery with the 2.0 V EMF.

Note: We will discuss matrix based methods in class to solve systems of linear equations such as those generated for this circuit. You may use your calculators to implement these methods.

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