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is described in Chapter 31.) When an excessive leakage current is detected, the current is shut off in less than 1 ms.
Chapter 28
Direct-Current Circuits
Summary
Definition
The emf of a battery is equal to the voltage across its terminals when the current is zero. That is, the emf is equivalent to the open-circuit voltage of the battery.
Concepts and Principles
The equivalent resistance of
a set of resistors connected in a
series combination is
R eq 5 R 1 1 R 2 1 R 3 1 ? ? ? (28.6)
The equivalent resistance of a set
of resistors connected in a parallel combination is found from the
relationship
1
1
1
1
5
1
1
1 c (28.8)
Req
R1
R2
R3
Circuits involving more than one loop are conveniently analyzed with
the use of Kirchhoff’s rules:
1. Junction rule. At any junction, the sum of the currents must
equal zero:
a I50
2. Loop rule. The sum of the potential differences across all elements around any circuit loop must be zero:
a
i 1t 2 5
e e2t/RC
R
When a resistor is traversed in the direction of the current, the potential
difference DV across the resistor is 2IR. When a resistor is traversed in the
direction opposite the current, DV 5 1IR. When a source of emf is traversed in the direction of the emf (negative terminal to positive terminal),
the potential difference is 1e. When a source of emf is traversed opposite
the emf (positive to negative), the potential difference is 2e.
(28.14)
(28.15)
where Q max 5 C e is the maximum charge on the capacitor.
The product RC is called the time constant t of the circuit.
Objective Questions
(28.10)
DV 5 0
closed loop
If a capacitor is charged with a battery through a
resistor of resistance R , the charge on the capacitor and
the current in the circuit vary in time according to the
expressions
q(t) 5 Q max(1 2 e2t/RC )
(28.9)
junction
If a charged capacitor of capacitance C is discharged through a resistor of resistance R, the
charge and current decrease exponentially in time
according to the expressions
q(t) 5 Q ie2t/RC
i 1t 2 5 2
Qi
RC
e2t/RC
(28.18)
(28.19)
where Q i is the initial charge on the capacitor and
Q i /RC is the initial current in the circuit.
1. denotes answer available in Student Solutions Manual/Study Guide
1. Is a circuit breaker wired (a) in series with the device it
is protecting, (b) in parallel, or (c) neither in series or
in parallel, or (d) is it impossible to tell?
2. A battery has some internal resistance. (i) Can the
potential difference across the terminals of the battery be equal to its emf? (a) no (b) yes, if the battery
is absorbing energy by electrical transmission (c) yes,
if more than one wire is connected to each terminal
(d) yes, if the current in the battery is zero (e) yes, with
no special condition required. (ii) Can the terminal
voltage exceed the emf? Choose your answer from the
same possibilities as in part (i).