PHY2049 recitation notes – week 8
Ch 26 review:
1. Resistors in series and parallel: When several resistors are connected in series, the current
through all resistors is the same, the equivalent resistance is
𝑅𝑒𝑞 = 𝑅1 + 𝑅2 + 𝑅3 + ⋯
When several resistors are connected in parallel, the potential difference across all resistors
is the same, the equivalent resistance satisfies
1
𝑅𝑒𝑞
1
1
1
=𝑅 +𝑅 +𝑅 +⋯
1
2
3
2. Kirchhoff’s rules: Kirchhoff’s junction rule states that the algebraic sum of the currents
into any junction must be zero. Kirchhoff’s loop rule states that the algebraic sum of
potential differences around any loop must be zero.
∑ 𝐼 = 0 (Junction rule)
∑ 𝑉 = 0 (Loop rule)
3. R-C circuits: When a capacitor is charged by a battery in series with a resistor or discharges
through a resistor, the current and capacitor charge are not constant. During the charging:
𝑡
𝑡
𝑞 = 𝐶ℰ (1 − 𝑒 −𝑅𝐶 ) = 𝑄𝑓 (1 − 𝑒 −𝑅𝐶 )
𝑖=
𝑑𝑞 ℰ −𝑡/𝑅𝐶
= 𝑒
= 𝐼0 𝑒 −𝑡/𝑅𝐶
𝑑𝑡 𝑅
During the discharging:
𝑞 = 𝑄0 𝑒−𝑡/𝑅𝐶
𝑖=
𝑑𝑞
𝑄0 − 𝑡
=−
𝑒 𝑅𝐶 = 𝐼0 𝑒−𝑡/𝑅𝐶
𝑑𝑡
𝑅𝐶
The time constant 𝜏 = 𝑅𝐶 is a measure of how quickly the capacitor charges or
discharges.
Examples:
1. Two identical light bulbs, each with resistance 𝑅 = 2 Ω, are connected to a source with
ℰ = 8 V and negligible internal resistance. Find the current through each bulb, the
potential difference across each bulb, and the power delivered to each bulb and to the
entire network if the bulbs are connected (a) in series and (b) in parallel. (c) Suppose one
of the bulbs burns out: that is, its filament breaks and current can no longer flow through
it. What happens to the other bulb in the series case? In the parallel case?
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2. Consider the circuit shown below. The emf of the battery is ℰ = 100 V. What are the
currents through 6.00-Ω resistor and 20.0-Ω resistor?
3. The figure below shows a “bridge” circuit. Find the current in each resistor and
equivalent resistance of the network of five resistors.
4. In the circuit shown blow, the batteries have negligible internal resistance and the meters
are both idealized. With the switch S open, the voltmeter reads 30.0 V.
(a) Find the emf ℰ of the battery.
(b) What will the ammeter read when the switch is closed?
5. In the circuit shown in the figure below, 𝐶 = 6.00 𝜇F, ℰ = 28.0 V, and the emf has
negligible resistance. Initially the capacitor is uncharged and the switch S is in position 1.
The switch is then moved to position 2, so that the capacitor begins to charge.
(a) What will be the charge on the capacitor a long time after the switch is moved to
position 2?
(b) After the switch has been in position 2 for 3.00 ms, the
charge on the capacitor is measured to be 110 𝜇C. What is
the value of the resistance R?
(c) How long after the switch is moved to position 2 will the
charge on the capacitor be equal to 99.0% of the final value
found in part (a)?
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