HW#4 Solutions Physics 2B
Dr. Stolovy
Ch. 18: 1, 5, 7, 15, 19, 27, 31, 33, 35, 37
18.1
From
18.5
(a)
, the internal resistance is
The equivalent resistance of the two parallel resistors is
Thus,
(b)
, so
Also,
Then,
and
18.7
When connected in series, we have
[1]
which we may rewrite as
[1a]
When in parallel,
or
[2]
Substitute Equations [1] and [1a] into Equation [2] to obtain:
or
[3]
Using the quadratic formula to solve Equation [3] gives
1
with two solutions of
and
Then Equation [1a] yields
or
Thus, the two resistors have resistances of
18.15
(a)
Connect
.
to get
combination
. Then connect that parallel
for a total resistance of
(b) Connect
to get
Also,
.
to get
Then,
18.19
.
.
to obtain
.
Consider the circuit diagram at the right, in which Kirchhoff’s junction rule has already
been applied at points a and e.
Applying the loop rule around loop abca gives
or
[1]
Next, applying the loop rule around loop cedc gives
or
[2]
Finally, applying the loop rule around loop caec gives
or
[3]
Substituting Equations [1] and [2] into Equation [3] yields
Thus, if
is
, the current in the wire between a and e
2
18.27
(a)
This multi-loop circuit does not contain any resistors in series (i.e., connected
so all the current in one must pass through the other) nor in parallel (connected so
the voltage drop across one is always the same as that across the other). Thus, this
circuit cannot be simplified any further, and Kirchhoff’s rules must be used to
analyze it.
(b) Assume currents
in the directions shown. Then, using Kirchhoff’s
junction rule at junction a gives
[1]
Applying Kirchhoff’s loop rule on the lower loop,
or
[2]
and for the loop around the perimeter of the circuit,
or
[3]
Substituting Equations [2] and [3] into [1]:
which reduces to
and gives
Then, Equation [2] gives
.
, and from Equation [3],
.
All currents are in the directions indicated in the circuit diagram given above.
18.33
(a)
The time constant of an RC circuit is
. Thus,
(b)
(c) To obtain the current through the resistor at time t after the switch is closed, recall
that the charge on the capacitor at that time is
and the potential
difference across a capacitor is
. Thus,
3
Then, considering switch S to have been closed at time
loop rule around the circuit shown above to obtain
, apply Kirchhoff’s
or
The current in the circuit at time t after the switch is closed is then
the current in the resistor at
is
18.35
(a)
The charge remaining on the capacitor after time t is
Thus, if
, then
and
.
,
or
(b)
18.37
, so
The current drawn by a single 75-W bulb connected to a 120-V source is
. Thus, the number of such bulbs that can be connected in
parallel with this source before the total current drawn will equal 30.0 A is
4
, so