# Electric currents dc currents, Kirchhoff`s rules

```Dr. Fritz Wilhelm; Homework 230
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E:\Excel files\230 lecture\ch28homework.docx; last saved: 12/31/2008 12:38:00
Electric currents dc currents, Kirchhoff’s rules.
V    rI
Electromotive force:
1. A battery has an emf of 15.0V. The terminal voltage of the battery is
11.6V when it is delivering 20.0 W of power to an external resistor R.
a) What is the value of R? b) What is the value for the internal resistance of
the battery? R=6.73Ω ; r=1.97 Ω
2.
The current in a loop circuit that has a resistance of R1 is 2.00A. The
current is reduced to 1.60A when an additional resistor of 3.00Ohm is
added in series to the first resistor. What is the value of R1 ? (12 Ω).
3. (7) Find a) the current in the 20Ω resistor and b) the potential difference
between the points a and b.
10Ω
5Ω
a
25V
b
10Ω
5Ω
20Ω
(ΔVab =5.68V, i=227mA)
4. (9) Consider the circuit below:
The maximum power that can safely be delivered to any of the three 100Ω
resistors is 25.0W. a) What is the maximum voltage that can be applied to the
terminals a and b? b) For this voltage determined in part a) what is the power
delivered to each resistor and what is the total power delivered?
100Ω
a
100Ω
b
100Ω
(a) ΔVmax =75V; b)37.5W total power; 25W through first resistor, 6.25W to the
resistors in parallel.
Dr. Fritz Wilhelm; Homework 230
Page 2 of 2
E:\Excel files\230 lecture\ch28homework.docx; last saved: 12/31/2008 12:38:00
Kirchhoff’s rules
5. (21) Determine the current in each branch of the circuit below: (I1
=846mA, I2 =462mA, I3 =1.31A)
8Ω
3Ω
 I2
1Ω
12V
 I1
6Ω
 I3
4V
RC circuits:
6. (27) Consider an RC circuit with R=1.00MΩ , C=5.00μF, and ε=30.0V
Find a) the time constant of the circuit and b) the maximum charge on the capacitor after
the switch is closed, c) the current in the resistor 10.0s after the switch is closed. (a)5.00s;
b)150μC; c)4.06μA
7.
A fully charged capacitor stores energy U0 How much energy remains
when its charge has decreased to half its original value.
(1/4 U0 )
8. (39) A 4.00MΩ resistor and a 3.00μF capacitor are connected in series
with a 12.0V power supply. a) Find the time constant of the circuit. b)
Express the current in the circuit and the charge on the capacitor as
functions of time, i.e. derive the differential equation and solve it for the
charging of the capacitor from 0 to its maximum. a) 12s; b)
q  36.0C(1  et /12 s ); I  3.00 Aet /12 s
```