DC CIRCUITS
BIG IDEA 1: Objects and systems have properties such as mass and charge. Systems may have
internal structure.
The student is able to make claims about natural phenomena based on conservation of electric charge.
The student is able to make predictions, using the conservation of electric charge, about the sign and relative
quantity of net charge of objects or systems after various charging processes, including conservation of
charge in simple circuits.
The student is able to choose and justify the selection of data needed to determine resistivity for a given
material.
BIG IDEA 5: Changes that occur as a result of interactions are constrained by conservation laws.
The student is able to construct or interpret a graph of the energy changes within an electrical circuit with
only a single battery and resistors in series and/or in, at most, one parallel branch as an application of the
conservation of energy (Kirchhoff’s loop rule).
The student is able to apply conservation of energy concepts to the design of an experiment that will
demonstrate the validity of Kirchhoff’s loop rule (∑ΔV=0) in a circuit with only a battery and resistors
either in series or in, at most, one pair of parallel branches.
The student is able to apply conservation of energy (Kirchhoff’s loop rule) in calculations involving the total
electric potential difference for complete circuit loops with only a single battery and resistors in series
and/or in, at most, one parallel branch.
The student is able to apply conservation of electric charge (Kirchhoff’s junction rule) to the comparison of
electric current in various segments of an electrical circuit with a single battery and resistors in series and in,
at most, one parallel branch and predict how those values would change if configurations of the circuit are
changed.
The student is able to design an investigation of an electrical circuit with one or more resistors in which
evidence of conservation of electric charge can be collected and analyzed.
The student is able to use a description or schematic diagram of an electrical circuit to calculate unknown
values of current in various segments or branches of the circuit.
1. ε = 24 V
a) What is the current passing though the 20 Ω resistor?
b) What is rate of thermal energy dissipated in the 30 Ω resistor?
2. Answer the following questions about the system of resistors above.
a) Calculate the equivalent resistance RXY.
b) If the circuit is connect to and external power source with a 9 volt potential, what is the current in the 3
Ω resistor?
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3. Three resistors are arranged in a circuit as shown above. The battery has an unknown but constant emf ε
and a negligible internal resistance.
(a) Rank the current in the three resistors from high to low: I1, I2, and I3.
(b) Determine the equivalent resistance of the three resistors.
The current I in resistor R3 is 0.40 ampere.
(c) Determine the emf ε (Voltage) of the battery.
(d) Determine the potential difference across resistor R1
(e) Determine the power dissipated in resistor R1
(f) Determine the amount of charge that passes through resistor R3 in one minute.
4. The circuit shows four identical bulbs connected to an ideal battery, which has negligible internal
resistance.
a) While the switch is closed, rank the brightness of the bulbs from greatest to least. Justify your answer.
b) With the switch open, rank the brightness of the bulbs from greatest to least. Justify your anwer.
5. Consider a circuit with three identical bulbs, an ideal battery, and a switch S. Each bulb has a resistance
of 120 Ω and the circuit is connected to a 24 V power source. Calculate the ratio of the current in i2
when the switch is closed to when it is open.
6. A student is asked to design a circuit to supply an electric motor with 1.0 mA of current at 3.0 V
potential difference.
a) Determine the power to be supplied to the motor.
b) Determine the electrical energy to be supplied to the motor in 60 s.
c) Determine the charge passing through the motor in 60 s.
d) Operating as designed above, the motor can lift a 0.012 kg mass a distance of 1.0 m in 60 s at constant
velocity. Determine the efficiency of the motor.
3. The circuit above contains a battery with negligible internal resistance, a closed switch S, and three
resistors, each with a resistance of R or 2R.
(a)
i.
Rank the currents in the three resistors from greatest to least, with number 1 being greatest. If two
resistors have the same current, give them the same ranking.
____ IA
ii.
____ IB
____ IC
Justify your answers.
(b)
i.
Rank the voltages across the three resistors from greatest to least, with number 1 being greatest. If
two resistors have the same voltage across them, give them the same ranking.
____ VA
ii.
Justify your answers.
____ VB
____ VC
For parts (c) through (e), use ε = 12 V and R = 200 Ω.
(c) Calculate the equivalent resistance of the circuit.
(d) Calculate the current in resistor RC.