Chapter 18 Direct Current Circuits Current Resistance and

Chapter 18 Direct Current Circuits

Current, Resistance, and Power Ch 17, Secs 1– 4, 6 DC Circuits and RC Circuits Ch 18, Secs 1– 3, 5 General Physics

1. 2. 3. 4. Which of the 4 circuits will light the bulb? A B C D 1 2 3 4 5 6 7 8 9 10 21 22 23 24 25 26 27 28 29 30 11 12 13 14 15 16 General 17 10 18 19 20 Physics

Sources of emf u The source that maintains the current in a closed circuit is called a source of emf • Any devices that increase the potential energy of charges circulating in circuits are sources of emf • Examples include batteries and generators u SI units are Volts • The emf is the work done per unit charge General Physics

emf & Internal Resistance u u A real battery has some internal resistance The schematic shows the internal resistance, r The terminal voltage is not equal to the emf because voltage drops across the internal resistance The terminal voltage is: ΔV = Vb-Va = ε – Ir Active Figure: A Real Battery General Physics

Resistors in Series u u u When two or more resistors are connected end-to-end, they are said to be in series The current is the same in all resistors because any charge that flows through one resistor flows through the others The sum of the potential differences across the resistors is equal to the total potential difference across the combination General Physics

Resistors in Series, cont u u u The current is the same in all resistors • I 1 = I 2 = I The total potential difference is equal to the sum of the potential differences across the resistors • ΔV 1 + ΔV 2 = ΔV The resistors can be replaced with one resistor with a resistance of • Req = R 1 + R 2 + … The equivalent resistor must have exactly the same external effect on the circuit as the original series resistors The equivalent resistance of a series combination of resistors is greater than any of the individual resistors General Physics

Equivalent Resistance – Series: An Example u Four series resistors are replaced with their equivalent resistance Active Figure: Resistors Connected in Series General Physics

Resistors in Parallel u u u When two or more resistors are connected across each other, they are said to be in parallel The potential difference across each resistor is the same because each is connected directly across the battery terminals The sum of the currents through the resistors is equal to the total current through the combination General Physics

Resistors in Parallel, cont u u u The total current is equal to the sum of the currents in the resistors • I 1 + I 2 = I The potential difference across the resistors is the same • ΔV 1 = ΔV 2 = ΔV The resistors can be replaced with one resistor with a resistance of • 1/Req = 1/R 1 + 1/R 2 + … The equivalent resistor must have exactly the same external effect on the circuit as the original parallel resistors The equivalent resistance of a parallel combination of resistors is less than the smallest of the individual resistors General Physics

Equivalent Resistance – Parallel: An Example u Three parallel resistors are replaced with their equivalent resistance Active Figure: Resistors Connected in Parallel General Physics

Problem-Solving Strategy, 1 u Combine all resistors in series • They carry the same current • If the resistors are different, the potential differences across them are not the same • The resistors add directly to give the equivalent resistance of the series combination: Req = R 1 + R 2 + … General Physics

Problem-Solving Strategy, 2 u Combine all resistors in parallel • The potential differences across them are the same • If the resistors are different, the currents through them are not the same • The equivalent resistance of a parallel combination is found through reciprocal addition: 1/Req = 1/R 1 + 1/R 2 + … General Physics

Problem-Solving Strategy, 3 u A complicated circuit consisting of several resistors and batteries can often be reduced to a simple circuit with only one resistor • Replace any resistors in series or in parallel using steps 1 or 2. • Sketch the new circuit after these changes have been made • Continue to replace any series or parallel combinations • Continue until one equivalent resistance is found General Physics

Problem-Solving Strategy, 4 u If the current in or the potential difference across a resistor in the complicated circuit is to be identified, start with the final circuit found in step 3 and gradually work back through the circuits • Use ΔV = I R and the procedures in steps 1 and 2 General Physics

Equivalent Resistance – Complex Circuit General Physics

How bright will each light be after adding one in parallel? 10 1. 2. 3. The same as before Brighter than before Dimmer than before 1 2 3 4 5 6 7 8 9 10 21 22 23 24 25 26 27 28 29 30 11 12 13 14 15 16 General 17 18 19 20 Physics

How bright will each light be after adding one in series? 10 1. 2. 3. The same as before Brighter than before Dimmer than before 1 2 3 4 5 6 7 8 9 10 21 22 23 24 25 26 27 28 29 30 11 12 13 14 15 16 General 17 18 19 20 Physics

RC Circuits u u A direct current circuit may contain capacitors and resistors – the current will vary with time When the circuit is completed, the capacitor starts to charge The capacitor continues to charge until it reaches its maximum charge (Q = Cε) Once the capacitor is fully charged, the current in the circuit is zero General Physics

Charging Capacitor in an RC Circuit u The charge on the capacitor varies with time • q = Q(1 – e-t/RC) • The time constant, =RC u The time constant represents the time required for the charge to increase from zero to 63. 2% of its maximum Active Figure: Charging a Capacitor General Physics

Notes on Time Constant In a circuit with a large time constant, the capacitor charges very slowly u The capacitor charges very quickly if there is a small time constant u After t = 10 , the capacitor is over 99. 99% charged u General Physics

Discharging Capacitor in an RC Circuit u u When a charged capacitor is placed in the circuit, it can be discharged The charge decreases exponentially • q = Qe-t/RC u At t = = RC, the charge decreases to 0. 368 of Qmax • In other words, in one time constant, the capacitor loses 63. 2% of its initial charge Active Figure: Discharging a Capacitor General Physics

Electrical Safety u u u Electric shock can result in fatal burns Electric shock can cause the muscles of vital organs (such as the heart) to malfunction The degree of damage depends on • • • the the magnitude of the current length of time it acts part of the body through which it passes General Physics

Effects of Various Currents u 5 m. A or less • Can cause a sensation of shock • Generally little or no damage u 10 m. A • Hand muscles contract • May be unable to let go a of live wire u 100 m. A • If passes through the body for just a few seconds, can be fatal General Physics

Electrical Signals in Neurons u Specialized cells in the body, called neurons, form a complex network that receives, processes, and transmits information from one part of the body to another General Physics

Electrical Signals in Neurons, cont u Three classes of neurons • Sensory neurons u Receive stimuli from sensory organs that monitor the external and internal environment of the body • Motor neurons u Carry messages that control the muscle cells • Interneurons u A simple neural circuit Transmit information from one neuron to another Electron microscope image of neurons in the brain General Physics