28_physics-ii_chapter28_direct_current_circuits-donusturuldu.pdf

CHAPTER 28 DIRECT CURRENT CIRCUITS
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ELECTROMOTIVE FORCE
In previous chapter, we discussed a circuit in which a battery produces a current. We will
generally use a battery as a source of energy for circuits in our discussion. Because the potential
difference at the battery terminals is constant in a particular circuit, the current in the circuit is
constant in magnitude and direction and is called direct current .
A battery is called source of electromotive force or, source of emf. The emf 𝜺 of a battery is the
maximum possible voltage that the battery can provide between its terminals . When an electric
potential difference exists between two points, the source moves charges from the lower
potential to the higher.
The connecting wires are assumed to have no resistance. The positive terminal of the battery is at
a higher potential than the negative terminal. In a real battery there is an internal resistance ? .

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Circuit diagram of a source of emf
with internal resistance r connected
to an external resistor of resistance R .
Passing from the negative terminal to the positive terminal, the
potential increases by an amount 𝜀 .
When we move through the resistance ? , the potential decreases by an
amount ?? , where ? is the current in the circuit. Thus, the terminal
voltage of the battery
∆? = ?
?
− ?
?
= 𝜀 − ?? = ??
𝜀 is equivalent to the open-circuit voltage-that is, the terminal voltage
when the current is zero.
?? = 𝜀 − ?? → ? =
𝜀
? + ?
The current depends on both the load resistance ? and the internal
resistance ? . If ? is much greater than ? ( R ≫ ? ), we can neglect ? .
Figure b is a graphical representation of the changes in electric potential
as the circuit is traversed in the clockwise direction. By inspecting Figure
a, we see that the terminal voltage Δ? must equal the potential
difference across the external resistance ? , often called the load
resistance.
Graphical representation showing how
the electric potential changes as the
circuit in part (a) is traversed clockwise.

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If we multiply equation 𝜀 = ?? + ?? by the current ? , we obtain
?𝜀 = ?
2
? + ?
2
?
This equation indicates that, because power ? = ?∆? , the total power output ?𝜀 of the
battery is delivered to the external load resistance in the amount ?
2
? and to the internal
resistance in the amount ?
2
? .

b) The power delivered to the load resistor is
Example 28.1: Terminal Voltage of a Battery
A battery has an emf of 12.0 ? and an internal resistance of 0.05 Ω . Its terminals are connected to a
load resistance of 3.00 Ω . (a) Find the current in the circuit and the terminal voltage of the battery.
(b) Calculate the power delivered to the load resistor, the power delivered to the internal resistance
of the battery, and the power delivered by the battery.
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Example 28.1:Continue … .