Example 25.2 provides an analysis of a real battery with internal resistance. The device attached across the terminals (see the diagram) is called the "load." The voltage across the terminals is also the voltage across out device (RL, the load.) Use the same values for the ideal battery voltage and internal resistance as in the example (12 V and 0.02 2 respectively.) Find voltage across the terminals, the current, and the power dissipated in the load when the load resistance is RL 1k, much larger than the internal resistance. Report all your results to 2 significant figures. = Find voltage across the terminals, the current, and the power dissipated in the load when the load resistance is 1m, much smaller than the internal resistance. Report all your results to 2 significant figures. For what ratio of RL/Rint (load over internal resistance) is the power to the load maximum? (It might help you to plot the power as a function of x = = RL/Rint.) EXAMPLE 25.5 Charging Capacitors: A Camera Flash Worked Example with Variation Problems A camera flash gets its energy from a 150-µF capacitor and requires 170 V to fire. If the capacitor is charged by a 200-V source through an 18-k resistor, how long must the photographer wait between flashes? Assume the capacitor is fully discharged with each flash. INTERPRET This is a problem about a charging capacitor, and we want to find the time to reach a given voltage. DEVELOP Equation 25.6, Vc = E(1 - eRC), gives the voltage across a charging capacitor, so our plan is to solve this equation for the time t. EVALUATE First we solve for the exponential term that contains the time: et/RC = 1 - Vc E Then we take the natural logarithm of both sides, recalling that In e* = x, so t RC-1 (1-1) In Solving for t and setting Vc = 170 V, E = 200 V, R = 18 k2, and C = 150 µF gives -RC In (1-1)=5 t= ln s ASSESS The time constant here is RC = 2.7 s, and 170 V is well over two-thirds of the 200-V source. Therefore, we expect a charging time longer than one time constant. Our 5.1-s answer is nearly 2RC. Problem 72 explores energy and power in this circuit.