A+ Answers

1) The circuit below consists of a group of external 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.