Download Electric Circuits 2

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Electric Circuits 2
 Electric circuit is a set of electrical components connected such that they provide
one or more complete paths for the movement of charges
 The switch in a circuit must be closed for a steady electric current to exist
 The filament of a light bulb acts as a resistor; charges moving through the
filament are slowed down, releasing their energy; the filament heats up and glows
 The simplest electric circuit is made up of a battery, a switch, two wires and a bulb
 Without a bulb or a resistor, the circuit contains little resistance to the movement
of the charges; this situation can be hazardous and is called a short circuit
 A series circuit describes two or more components of a circuit that provide a
single path for current
 An ammeter should always be connected in series to measure the current
 For a series circuit the equivalent resistance is the sum of the circuit’s resistances:
𝑅�� = 𝑅� + 𝑅� + 𝑅� + ⋯
 For a series circuit the current at any part of the circuit is the same:
𝐼 = 𝐼� = 𝐼� = 𝐼� = ⋯
 For a series circuit the potential rise in the battery equals the sum of potential
drops in the resistances:
𝑉 = 𝑉� + 𝑉� + 𝑉� + ⋯
 A parallel circuit describes two or more components of a circuit that provide
separate conducting paths for current because the components are connected
across common points or junctions
 A voltmeter should always be connected in parallel to measure voltage
 For a parallel circuit the reciprocal of the equivalent resistance is the sum of the
reciprocals of circuit’s resistances:
1
1
1
1
=
+
+
+⋯
𝑅�� 𝑅� 𝑅� 𝑅�
 For a parallel circuit the total current equals the sum of the currents in resistors:
𝐼 = 𝐼� + 𝐼� + 𝐼� + ⋯
 For a parallel circuit the terminal voltage is the same as the potential drops at any
of the resistors in the circuit:
𝑉 = 𝑉� = 𝑉� = 𝑉� = ⋯
 Because of the reciprocal relationship, the equivalent resistance for a parallel
circuit must always be less than the smallest resistance in the circuit
 For any junction the algebraic sum of currents going in is the same as the algebraic
sum of currents going out; in other words charges do not hang out in junctions
 Combined circuits can be understood by isolating segments that are in series or
in parallel and simplifying them to their equivalent resistances
SERIES CIRCUITS
1.
Three resistors are connected in series across a 120-V generator.
a. What is the equivalent resistance of the circuit?
b. What is the current in the circuit?
2.
A 9-V battery is in a circuit with three resistors in series.
a. If the resistance of one of the resistors increases, how will
the equivalent resistance change?
b. What will happen to the current?
c. Will there be any change in the battery voltage?
3. Two resistors, 47.0- Ω and 82.0- Ω are connected in series across
a 45.0V battery as shown in the picture.
a. What is the current in the circuit?
b. What is the voltage drop across resistors?
c. If the 47.0- Ω resistor is replaced by a
39.0- Ω resistor, will the current increase,
decrease or remain the same?
d. What is the new voltage drop across the 82.0- Ω?
4.
In the picture the voltmeter reads 70.0 V.
a. Which resistor is the hottest?
b. Which resistor is the coolest?
c. What will the ammeter read?
d. What is power supplied by the battery?
PARALLEL CIRCUITS
5. Three 15.0-Ω resistors are connected in parallel and placed across
a 30.0-V battery.
a. What is the equivalent resistance of the parallel circuit?
b. What is the current through the entire circuit?
c. What is the current through each branch of the circuit?
6. Three resistors, 60.0 Ω, 30.0 Ω, and 20.0 Ω, are connected in
parallel across a 90.0-V battery.
a. Find the current through each branch.
b. Find equivalent resistance of circuit.
c. Find the current through the battery.
7. A 150- Ω branch in a circuit must be reduced to 93 Ω. A resistor
will be added to this branch of the circuit to make this change. What
value of the resistance should be used and how must the resistor be
connected?
8.
The battery in the picture below develops 110 V.
a. Which resistor is the hottest?
b. Which resistor is the coolest?
c. What will ammeter 1 read?
d. What will ammeter 2 read?
e. What will ammeter 3 read?
f. What will ammeter 4 read?