CHAPTER 28 661
The emf is the energy (work done going through the source from the negative to the positive terminal) per unit charge:
E=⋅× =()( ) ( ) .50 3600 3 10 6
W h s/h C V= (This is the average emf; the actual emf may vary with time.)
Section 28-3: Simple Circuits: Series and Parallel Resistors
resistor and a
resistor are in parallel, and the pair is in series with a
resistor. What is the
resistance of the combination?
From Equations 28-1 and 3c,
9. What resistance should be placed in parallel with a
resistor to make an equivalent resistance of
The solution for R2 in Equation 28-3a is
2 1 1 56 45 56 45 229
parallel parallel k k .= =( ) ( )( ) ( )
10. In Fig. 28-49 all resistors have the same value, R. What will be the resistance measured (a) between A and B or
(b) between A and C?
FIGURE 28-49 Problems 10 and 11.
(a) The resistance between A and B is equivalent to two resistors of value R in series with the parallel combination of
resistors of values R and 2R. Thus,
= = (b)
is equivalent to just one resistor of
value R in series with the parallel combination of R and 2R (since the resistor at point B carries no current, i.e., its branch is
an open circuit). Thus
11. In Fig. 28-49, take all resistors to be
. If a 6.0-V battery is connected between points A and B, what will be the
current in the vertical resistor?
The circuit in Fig. 28-49, with a battery connected across points A and B, is similar to the circuit analysed in Example 28-4.
In this case, R|| ()( ) ( ) ( ) ,= + =1 2 1 2 2
Ω Ω= and Rtot = + + =1 1 2
Ω Ω Ω Ω. The total current (that through the battery)
tot tot V A= = =E= =68
( ) ( ) .Ω The voltage across the parallel combination is IR
tot A V
|| ()( ),= =
Ω which is
the voltage across the vertical
resistor. The current through this resistor is then ( ) ( ) . .
1 15V A