Physics 2080
Homework 4
1. The bulbs in the circuit shown are identical. Treat the battery as ideal in answering
all questions.
a. Rank the bulbs 1-6 in order of brightness. Explain your
reasoning.
b. Rank the voltages across the bulbs. Explain your
reasoning.
c. Write an equation that relates the voltage across bulbs 3, 5,
and 6 to the battery voltage.
d. Bulb 1 is removed from its socket.
i. Does the brightness of bulb 2 increase, decrease, or
remain the same? Explain.
ii. Does the brightness of bulb 6 increase, decrease, or
remain the same? Explain.
iii. Does the brightness of bulb 3 increase, decrease, or remain the same? Explain.
2. The circuit at right contains a battery, a bulb, a switch,
and a capacitor. The capacitor is initially uncharged.
a. Describe the behavior of the bulb in the two situations
below.
i. The switch is first moved to position 1. Describe
the behavior of the bulb from just after the switch
is closed until a long time later. Explain.
ii. The switch is now moved to position 2. Describe the behavior of the bulb
from just after the switch is closed until a long time later. Explain your
reasoning.
b. A second identical bulb is now added to the circuit as
shown. The capacitor is discharged.
i. The switch is now moved to position 1. Describe the
behavior of bulbs B and C from just after the switch
is closed until a long time later. Explain. How does
the initial brightness of bulb C compare to the initial
brightness of bulb A in question (i) of part (a)? A
long time after the switch is closed, is the potential
difference across the capacitor greater than, less
than, or equal to the potential difference across the battery? Explain.
ii. The switch is now moved to position 2. Describe the behavior of bulbs B and
C from just after the switch is closed until a long time later. Explain your
reasoning. How does the initial brightness of bulb C compare to the initial
brightness of bulb A in question (ii) of part (a)? Explain your reasoning.
iii. A long time after the switch is closed, is the potential difference across the
capacitor greater than, less than, or equal to the potential difference across the
battery? Explain.
3. For the following circuits, use Kirchoff’s rules to find the indicated quantities:
a. A set of batteries and bulbs are connected as shown.
All of the bulbs have resistance R and the current
through bulb C is I as indicated. Use Kirchoff’s rules
to find
i. the current through bulbs A and B and through the
battery
ii. the voltage drop across the battery
Express your answers in terms of R and I. In
explaining your arguments, explain which of the
Kirchoff principles you are using and how. If you have not used all of them,
discuss whether you are using the missing ones implicitly or whether they are not
relevant here.
b. An electrical circuit is connected as shown.
It contains two batteries. The battery labeled
#1 is rated at 6 V and the battery labeled #2
is rated at 6 V. The three bulbs, labeled A,
B, and C, can be taken to have almost a
constant resistance of 3 Ω. Use Kirchoff’s
rules to find
i. the current through each of the bulbs and
ii. the current through each of the batteries
In explaining your argument, explain which of the Kirchoff principles you are using
and how. If you have not used all of them, discuss whether you are using the missing
ones implicitly or whether they are not relevant here.
4. A 10 V battery is connected to a series RC circuit consisting of a resistor of 2.0 x 106
Ω and a capacitor of 3.0 µF. Find the time required for the charge on the capacitor to
reach 90% of its final value.
5. Find the current in each resistor in the circuit shown. V = 6V, R1 = 2.0 Ω, R2 = 4.0
Ω, and R3 = 8.0 Ω.
6. A circuit contains two resistors (10 Ω and 20
Ω) and two capacitors (12 µF and 6 µF)
connected to a 6V battery, as shown. The
circuit has been connected for a long time.
a. Calculate the total capacitance of the
circuit.
b. Calculate the current in the 10 Ω resistor.
c. Calculate the potential difference between
points A and B.
d. Calculate the charge stored on one plate of the 6 µF capacitor.
e. The wire is cut at point P. Will the potential difference between points A and B
increase, decrease, or remain the same? Explain your answer.
For this problem, it may be helpful to create the circuit on the AC+DC Circuit
Construction Kit simulation used in class. When building the circuit, keep the
electrons turned on to help you trace the current in the circuit and see what happens to
each of the branches as the capacitors charge. There is a link to the simulations on
the Links sidebar on the course website.