University Physics Volume 2

# Summary

### 10.1Electromotive Force

• All voltage sources have two fundamental parts: a source of electrical energy that has a characteristic electromotive force (emf), and an internal resistance r. The emf is the work done per charge to keep the potential difference of a source constant. The emf is equal to the potential difference across the terminals when no current is flowing. The internal resistance r of a voltage source affects the output voltage when a current flows.
• The voltage output of a device is called its terminal voltage $VterminalVterminal$ and is given by $Vterminal=ε−IrVterminal=ε−Ir$, where I is the electric current and is positive when flowing away from the positive terminal of the voltage source and r is the internal resistance.

### 10.2Resistors in Series and Parallel

• The equivalent resistance of an electrical circuit with resistors wired in a series is the sum of the individual resistances: $Rs=R1+R2+R3+⋯=∑i=1NRiRs=R1+R2+R3+⋯=∑i=1NRi$.
• Each resistor in a series circuit has the same amount of current flowing through it.
• The potential drop, or power dissipation, across each individual resistor in a series is different, and their combined total is the power source input.
• The equivalent resistance of an electrical circuit with resistors wired in parallel is less than the lowest resistance of any of the components and can be determined using the formula
$Req=(1R1+1R2+1R3+⋯)−1=(∑i=1N1Ri)−1.Req=(1R1+1R2+1R3+⋯)−1=(∑i=1N1Ri)−1.$
• Each resistor in a parallel circuit has the same full voltage of the source applied to it.
• The current flowing through each resistor in a parallel circuit is different, depending on the resistance.
• If a more complex connection of resistors is a combination of series and parallel, it can be reduced to a single equivalent resistance by identifying its various parts as series or parallel, reducing each to its equivalent, and continuing until a single resistance is eventually reached.

### 10.3Kirchhoff's Rules

• Kirchhoff’s rules can be used to analyze any circuit, simple or complex. The simpler series and parallel connection rules are special cases of Kirchhoff’s rules.
• Kirchhoff’s first rule, also known as the junction rule, applies to the charge to a junction. Current is the flow of charge; thus, whatever charge flows into the junction must flow out.
• Kirchhoff’s second rule, also known as the loop rule, states that the voltage drop around a loop is zero.
• When calculating potential and current using Kirchhoff’s rules, a set of conventions must be followed for determining the correct signs of various terms.
• When multiple voltage sources are in series, their internal resistances add together and their emfs add together to get the total values.
• When multiple voltage sources are in parallel, their internal resistances combine to an equivalent resistance that is less than the individual resistance and provides a higher current than a single cell.
• Solar cells can be wired in series or parallel to provide increased voltage or current, respectively.

### 10.4Electrical Measuring Instruments

• Voltmeters measure voltage, and ammeters measure current. Analog meters are based on the combination of a resistor and a galvanometer, a device that gives an analog reading of current or voltage. Digital meters are based on analog-to-digital converters and provide a discrete or digital measurement of the current or voltage.
• A voltmeter is placed in parallel with the voltage source to receive full voltage and must have a large resistance to limit its effect on the circuit.
• An ammeter is placed in series to get the full current flowing through a branch and must have a small resistance to limit its effect on the circuit.
• Standard voltmeters and ammeters alter the circuit they are connected to and are thus limited in accuracy.
• Ohmmeters are used to measure resistance. The component in which the resistance is to be measured should be isolated (removed) from the circuit.

### 10.5RC Circuits

• An RC circuit is one that has both a resistor and a capacitor.
• The time constant $ττ$ for an RC circuit is $τ=RC.τ=RC.$
• When an initially uncharged capacitor in series with a resistor is charged by a dc voltage source, the capacitor asymptotically approaches the maximum charge.
• As the charge on the capacitor increases, the current exponentially decreases from the initial current: $I0=ε/R.I0=ε/R.$
• If a capacitor with an initial charge Q is discharged through a resistor starting at $t=0t=0$, then its charge decreases exponentially. The current flows in the opposite direction, compared to when it charges, and the magnitude of the charge decreases with time.

### 10.6Household Wiring and Electrical Safety

• The two types of electric hazards are thermal (excessive power) and shock (current through a person). Electrical safety systems and devices are employed to prevent thermal and shock hazards.
• Shock severity is determined by current, path, duration, and ac frequency.
• Circuit breakers and fuses interrupt excessive currents to prevent thermal hazards.
• The three-wire system guards against thermal and shock hazards, utilizing live/hot, neutral, and ground wires, and grounding the neutral wire and case of the appliance.
• A ground fault circuit interrupter (GFCI) prevents shock by detecting the loss of current to unintentional paths.
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