Internal Resistance Consider the following diagram: voltage battery

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Presentation transcript:

Internal Resistance Consider the following diagram: voltage battery Thus far we have referred to a battery as a source of _________ and we have made the assumption that the battery is an ideal source. An ideal __________ would be able to maintain the same _______________ _____________ between its terminals regardless of the current drawn. voltage battery potential difference Consider the following diagram: Internal resistance of the real battery + r r VT ε emf of the battery ε - Terminal voltage of the battery (the actual voltage applied to the external circuit) VT

ε = VT + Ir Which value is larger ε or VT? Why emf is larger because VT is the voltage put out by the battery after some of the emf has been ‘lost’ to the internal resistance Derive an expression that relates ε and VT (assume a current flows through the internal resistance) ε = VT + Ir Would the value of the resistance connected across the terminals of the battery effect the emf of the battery? Explain. No; emf is determined by the electrochemical processes within the battery

Would the value of the resistance connected across the terminals of the battery effect the terminal voltage of the battery? Explain. Yes; the bigger the resistance across the terminals of the battery, the smaller the current drawn and thus the bigger VT Would the value of the resistance connected across the terminals of the battery effect the internal resistance of the battery? Explain. No; internal resistance is determined by the makeup of the components of the battery

Practice Exercise ε = 15.0 V Given: ε RL = 2Ω PL = 72 watts Suppose a battery has an emf of 15.0 V. When a resistance of 2.0 ohms is placed across the battery terminals, 72 Watts is dissipated in the 2 ohm resistor. Determine the internal resistance of the battery. ε = 15.0 V RL = 2Ω PL = 72 watts Draw the circuit Given: Since 72 watts is dissipated in the 2Ω resistor, we can easily determine the voltage across this resistor r 2 Ω Find this value ε Real battery

ε = VT + Ir V= 12 V V2 V2 72 = P = 2 R terminal voltage VT = IT RT This is also the __________ _____________ of the battery. Use Ohm’s Law to determine the current through the circuit. VT = IT RT 12 = I (2) IT = 6 amps internal This is also the current flowing through the __________ _____________ of the battery. resistance Now that we know the emf, current, and terminal voltage, we can solve for the internal resistance of the battery. ε = VT + Ir r = 0.5Ω 15 = 12 + (6)r

Now solve for the power dissipated in the battery. P = IV P = (6)(3) = 18 watts Voltage across internal resistance. Current through internal resistance.