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2 class Noodle { 3 String name; 4 Noodle(String n) { name = n; } 5 } 6 class AsianNoodle extends Noodle { 7 public boolean equals(Object o) { 8 AsianNoodle n = (AsianNoodle)o; 9 if(nameequals(nname)) return true; 10 return false; 11 }

Figure 23-6 The parallel paths for current in this diagram are analogous to multiple paths that a river might take down a mountain



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120 V 38 A 24 5A A 120 V V 9 13 A A 120 V V 6 20 A A 120 V V Figure 23-7 In a parallel circuit, the total current is equal to the sum of the currents in the individual paths

Grover s equation (Grover, 1946) seems closer to the actual inductance measured in empirical tests than certain other equations that are in use This equation is L where L (K1 N 2a) ln K2a N (N 1) b K3 K4 (N 1) b aN





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What is the current through each resistor in a parallel electric circuit It depends upon the individual resistances For example, in Figure 23-7, the potential difference across each resistor is 120 V The current through a resistor is given by I V/R, so you can calculate the current through the 24- resistor as I (120 V)/(24 ) 50 A and then calculate the currents through the other two resistors The total current through the generator is the sum of the currents through the three paths, in this case, 38 A What would happen if the 6- resistor were removed from the circuit Would the current through the 24- resistor change That current depends only upon the potential difference across it and its resistance; because neither has changed, the current also is unchanged The same is true for the current through the 9- resistor The branches of a parallel circuit are independent of each other The total current through the generator, however, would change The sum of the currents in the branches would be 18 A if the 6- resistor were removed Resistance in a parallel circuit How can you find the equivalent resistance of a parallel circuit In Figure 23-7, the total current through the generator is 38 A Thus, the value of a single resistor that results in a 38-A current when a 120-V potential difference is placed across it can easily be calculated by using the following equation: R

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12 public int hashCode() { return namelength(); } 13 AsianNoodle(String s) { super(s); } 14 } 15 public class Soba extends AsianNoodle { 16 public static void main(String[] args) { 17 Noodle n1 = new Noodle("bob"); Noodle n2 = new Noodle("bob"); 18 AsianNoodle a1 = new AsianNoodle("fred"); 19 AsianNoodle a2 = new AsianNoodle("fred"); 20 Soba s1 = new Soba("jill"); Soba s2 = new Soba("jill"); 21 Systemoutprint(n1equals(n2) + " " + (n1 == n2) + " | "); 22 Systemoutprint(a1equals(a2) + " " + (a1 == a2) + " | "); 23 Systemoutprintln(s1equals(s2) + " " + (s1 == s2)); 24 } 25 Soba(String s) { super(s); } 26 }

32 Notice that this resistance is smaller than that of any of the three resistors in parallel Placing two or more resistors in parallel always decreases the equivalent resistance of a circuit The resistance decreases because each new resistor provides an additional path for current, thereby increasing the total current while the potential difference remains unchanged To calculate the equivalent resistance of a parallel circuit, first note that the total current is the sum of the currents through the branches If IA, IB, and IC are the currents through the branches and I is the total current, then I IA IB IC The potential difference across each resistor is the same, so the current through each resistor, for example, RA, can be found from IA V/RA Therefore, the equation for the sum of the currents is as follows:

Testing Resistance Ohmmeters, which are used to measure resistance, work by passing a known voltage across a resistor and measuring the current The resistance is then displayed Some ohmmeters use potentials of less than 1 V to avoid damaging delicate electronic components, whereas others may use hundreds of volts to check the integrity of insulating materials

Dividing both sides of the equation by V provides an equation for the equivalent resistance of the three parallel resistors Equivalent Resistance for Resistors in Parallel

The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances

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