CHAPTER28DIRECTCURRENTCIRCUITS1ELECTROMOTIVE FORCEIn previous chapter, we discussed a circuit in which a battery produces a current. We willgenerally use a battery as a source of energy for circuits in our discussion. Because the potentialdifference at the battery terminals is constant in a particular circuit, the current in the circuit isconstant in magnitude and direction and is calleddirect current.A battery is called source of electromotive force or, source of emf.The emf𝜺of a battery is themaximum possible voltage that the battery can provide between its terminals. When an electricpotential difference exists between two points, the source moves charges from the lowerpotential to the higher.The connecting wires are assumed to have no resistance. The positive terminal of the battery is ata higher potential than the negative terminal. In a real battery there is aninternal resistance?.
2Circuit diagram of a source of emfwith internal resistancerconnectedto an external resistor of resistanceR.Passingfromthenegativeterminaltothepositiveterminal,thepotentialincreasesby an amount𝜀.When we move through the resistance?, the potentialdecreasesby anamount??, where?is the current in the circuit. Thus, the terminalvoltage of the battery∆? = ??− ??= 𝜀 − ?? = ??𝜀is equivalent to the open-circuit voltage-that is, theterminal voltagewhen the current is zero.?? = 𝜀 − ?? → ? =𝜀? + ?The current depends on both the load resistance?and the internalresistance?. If?is much greater than?(R ≫ ?), we can neglect?.Figure b is a graphical representation of the changes in electric potentialas the circuit is traversed in the clockwise direction. By inspecting Figurea, we see that the terminal voltageΔ?must equal the potentialdifferenceacross theexternalresistance?,often calledtheloadresistance.Graphicalrepresentationshowinghowtheelectricpotentialchangesasthecircuit in part (a) is traversed clockwise.
3If we multiply equation𝜀 = ?? + ??by the current?, we obtain?𝜀 = ?2? + ?2?This equation indicates that, because power? = ?∆?, the total power output?𝜀of thebattery is delivered to the external load resistance in the amount?2?and to the internalresistance in the amount?2?.
b) The power delivered to the load resistor isExample 28.1:Terminal Voltage of a BatteryA battery has an emf of12.0 ?and an internal resistance of0.05 Ω. Its terminals are connected to aload resistance of3.00 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 resistanceof the battery, and the power delivered by the battery.4