Example 21.5 Terminal Voltage of a Battery A battery has an emf of 12.0 V and an internal resistance of 0.0200 0. Its terminals are connected to a load resistance of 3.00 0. ab [A) Find the current in the circuit and the terminal voltage of the battery. (B) Calculate the power delivered to the load resistor, the R power delivered to the internal resistance of the battery, and the power delivered by the battery. Circuit diagram of a source of emf & (in this case, a battery), of internal resistance r, connected to an external resistor of SOLVE IT resistance R. (A) Find the current in the circuit and the terminal voltage of the battery. Conceptualize Study the figure, which shows a circuit consistent with the problem statement. The battery delivers energy to the load resistor. Categorize This example involves simple calculations from this section, so we categorize it as a substitution problem. Find the current in the circuit: 12.0 V R+r 3.00 0 + 0.0200 0 Write expressions for the power through the load resistor and through both resistors combined in terms of the resistances and current. Then I = 3.97 VA Find the terminal voltage: AV = 8 - IF = 12.0 V - (1)(0.0200 n) = 11.92 v To check this result, calculate the voltage AV = IR = (1)(3.00 0) = 11.91 v v across the load resistance R: (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. Find the power delivered to the load PR = 12R = (1)2 (3.00 0) = 47.28 W resistor: Find the power delivered to the internal P, = 12r = (1)2 (0.0200 n) = 0.315 W resistance: Find the power delivered by the battery by P, = PR + P, = 47.60 w adding these quantities: MASTER IT HINTS: GETTING STARTED | I'M STUCK! With the internal resistance of 0.11 0, what will be the minimal load resistance to ensure at least 89 percent of the power delivered by the battery goes to the load? R = x 2