This circuit has two resistors, with \(R_1
\gt R_2\).
Which of the two resistors has greater current?
Which of the two resistors has greater voltage?
Which of the two resistors dissipates the larger amount of
power?
\(I_1 = I_2\)
\(V_1 \gt V_2\)
\(P_1 \gt P_2\)
c2. Power in parallel
resistors
This circuit has two resistors, with \(R_1
\gt R_2\).
Which of the two resistors has greater current?
Which of the two resistors has greater voltage?
Which of the two resistors dissipates the larger amount of
power?
\(I_2 \gt I_1\)
\(V_1 = V_2\)
\(P_2 \gt P_1\)
c3. Find the parellel
resistors
Consider the resistor network shown.
Resistor 8 is in parallel with which other resistor(s)?
Resistor 1 is in parallel with which other resistor(s)?
Resistor 7 is in parallel with which other resistor(s)?
6, 9, 5
2
4, 11
c4. Various resistor
networks
The figure shows five combinations of identical resistors. Rank in
order, from largest to smallest, the equivalent resistances \((R_{\rm{eq}})_1\) to \((R_{\rm{eq}})_5\)
Bulbs \(A\), \(B\) and \(C\) are identical. What would happen to all
bulbs (brighter, dimmer, go out) in the following cases?
Bulb \(C\) is cut free at points 1
and 2, leaving an open circuit.
A wire is connected between points 1 and 2.
\(C\) goes out, \(A\) gets dimmer, and \(B\) gets brighter
\(A\) gets brighter, \(B\) and \(C\) go out
Reasons: Bulb brightness depends on power: \(P = I^2 R = \frac{V^2}{R}\). A bulb’s
resistance won’t change, so if you can determine that either \(I\) or \(V\) increase for a bulb, then it will get
brighter.
Initially, \(A\) has more of the
voltage than \(B\) (more than half of
the battery voltage). Finally, \(A\)
and \(B\) both have one half of the
battery voltage. So \(V_A\) decreases
(\(A\) gets dimmer), and \(V_B\) increases (\(B\) gets brighter).
A wire from 1 to 2 is a zero-resistance parallel branch that will
short out \(B\) and \(C\) – they both go out. Overall circuit
resistance goes down, so \(A\) gets
brighter.
c6. Kirchoff’s Rules
Consider the circuit below with the current directions defined as
shown.
False. Need to include \(IR\) terms in \(\sum \Delta V\)
True. This is the corrected version of
b.
True. At lease one of these currents must be
negative.
Long Answer Questions
1. Homemade capacitor in an
RC circuit
A homemade capacitor is constructed of 2 sheets of aluminum foil with
an area of \(2.00\) square meters,
separated by paper, \(0.05\) mm thick,
of the same area and a dielectric constant of \(3.7\). The homemade capacitor is connected
in series with a \(100.00\) Ω resistor,
a switch, and a \(6.00\) V voltage
source.
What is the RC time constant of the circuit?
What is the initial current through the circuit, when the switch is
closed?
How long does it take the current to reach one third of its initial
value?
\(\displaystyle \tau = RC = R \left ( k
\epsilon_0 \frac{A}{d} \right ) = 0.131\) ms
A student makes a homemade resistor from a graphite pencil \(5.00\) cm long, where the graphite is \(0.05\) mm in diameter. The resistivity of
the graphite is \(\rho = 1.38 \times
10^{−5}\) Ω/m. The homemade resistor is placed in series with a
switch, a \(10.00\) mF capacitor and a
\(0.50\) V power source.
What is the RC time constant of the circuit?
What is the potential drop across the pencil \(1.00\) s after the switch is closed?
\(\tau = RC = 3.51\) s
\(V = 376\) mV
3. Resistor circuit with
switch
Consider the circuit shown.
Determine the equivalent resistance and the current from the battery
with switch \(S_1\) open.
Determine the equivalent resistance and the current from the battery
with switch \(S_1\) closed.
