An external resistor with resistance R is connected to a battery that has emf ε and internal resistance r. Let P be the electrical power output of the source. By conservation of energy, P is equal to the power consumed by R. What is the value of P in the limit that R is (a) very small; (b) very large? (c) Show that the power output of the battery is a maximum when R = r. What is this maximum P in terms of ε and r? (d) A battery has ε = 64.0 V and r = 4.00 Ω. What is the power output of this battery when it is connected to a resistor R, for R = 2.00 Ω, R = 4.00 Ω, and R = 6.00 Ω? Are your results consistent with the general result that you derived in part (b)?
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