Kirchhoff s laws. Objectives. Assessment. Assessment. Assessment. Assessment 5/27/14. Apply Kirchhoff s first and second laws.
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1 Kirchhoff s laws Objectives Apply Kirchhoff s first and second laws. Calculate the current and voltage for resistor circuits connected in parallel. Calculate the current and voltage for resistor circuits connected in series. 1. A current I = 4.0 amps flows into a junction where three wires meet. I 1 = 1.0 amp. What is I 2? 2. A 15 volt battery is connected in parallel to two identical resistors. a) What is the voltage across R 1? b) If R 1 and R 2 have different resistances, will they have different voltages? 3. Two 30.0 Ω resistors are connected in parallel with a 10-volt battery. a) What is the total resistance of the circuit? b) What is the voltage drop across each resistor? c) What is the current flow through each resistor? 4. Two 5.0 Ω resistors are connected in series with a 30-volt battery. a) What is the total resistance of the circuit? b) What is the current flow through each resistor? c) What is the voltage drop across each resistor? 1
2 Physics terms Equations junction loop Kirchhoff s laws: current law: voltage law: Kirchhoff s laws Two fundamental laws apply to ALL electric circuits. These are called Kirchhoff s laws, in honor of German physicist Gustav Robert Kirchhoff ( ). Kirchhoff s first law is the current law. It is a rule about electric current. It is always true for ALL circuits. The current law is also known as the junction rule. A junction is a place where three or more wires come together. This figure shows an enlargement of the junction at the top of the circuit. Current Io flows INTO the junction. Currents I 1 and I 2 flow OUT of the junction. What do you think the current law says about I, I 1, and I 2? 2
3 : The current flowing INTO a junction always equals the current flowing OUT of the junction. Example: Why is the current law true? Conservation of charge Why is this law always true? Why is this law always true? It is true because electric charge can never be created or destroyed. Charge is ALWAYS conserved. This series circuit has NO junctions. The current must be the same everywhere in the circuit. Current can only change at a junction. A 60 volt battery is connected to three identical resistors. What are the currents through the resistors? 60 V 3
4 A 60 volt battery is connected to three identical resistors. What are the currents through the resistors? R eq = 30 Ω 60 V This series circuit has two junctions. Find the missing current. I = 60 V / 30 Ω = 2 amps through each resistor? This series circuit has two junctions. Find the missing current. How much current flows into the upper junction? I 2 = 2 A 2 amps How much current flows into the upper junction? I = 4 A Kirchhoff s second law is the voltage law. It s a rule about voltage gains and drops. It is always true for ALL circuits. 4 amps 4
5 The voltage law is also known as the loop rule. A loop is any complete path around a circuit. This circuit has only ONE loop. Pick a starting place. There is only ONE possible way to go around the circuit and return to your starting place. This circuit has more than one loop. Charges can flow up through the battery and back through R 1. That s one loop. Can you describe a second loop that charges might take? This circuit has more than one loop. Charges can flow up through the battery and back through R 1. says that sum of the voltage gains and drops around any closed loop must equal zero. That s one loop. Can you describe a second loop that charges might take? Charges can flow up through the battery and back through R 2. That s another loop. If this battery provides a gain, what is the voltage drop across each resistor? If this battery provides a gain, what is the voltage drop across each resistor? Assume the resistors are identical. Assume the resistors are identical volts each! 5
6 A 60 V battery is connected in series with three different resistors. A 60 V battery is connected in series with three different resistors. Resistor R 1 has a 10 volt drop. Resistor R 2 has a 30 volt drop. What is the voltage across R 3? 60 V - Resistor R 1 has a 10 volt drop. Resistor R 2 has a 30 volt drop. What is the voltage across R 3? 60 V -? 20 volts -20 V What if a circuit has more than one loop? Treat each loop separately. The voltage gains and drops around EVERY closed loop must equal zero. A battery is connected in parallel with two resistors. What is the voltage across R 1? A battery is connected in parallel with two resistors. What is the voltage across R 1? A battery is connected in parallel with two resistors. What is the voltage across R 1? R 1 must have a drop. R 1 must have a drop. What is the voltage across R 2? 6
7 Why is the voltage law true? A battery is connected in parallel with two resistors. What is the voltage across R 1? R 1 must have a drop. Why is this law always true? What is the voltage across R 2? R 2 also has a drop. Why is the voltage law true? Conservation of energy Why is this law always true? This law is really conservation of energy for circuits. All the electric potential energy gained by the charges must equal the energy lost in one complete trip around a loop. All the electrical energy gained by passing through the battery is lost as charges pass back through the resistors. All the gravitational potential energy gained by going up a mountain is lost by going back to your starting place. 1. A current I = 4.0 amps flows into a junction where three wires meet. I 1 = 1.0 amp. What is I 2? 1. A current I = 4.0 amps flows into a junction where three wires meet. I 1 = 1.0 amp. What is I 2? Use the junction rule: I 2 = 3.0 amps 7
8 2. A 15 volt battery is connected in parallel to two identical resistors. a) What is the voltage across R 1? b) If R 1 and R 2 have different resistances, will they have different voltages? 2. A 15 volt battery is connected in parallel to two identical resistors. a) What is the voltage across R 1? 15 volts (use the loop rule) b) If R 1 and R 2 have different resistances, will they have different voltages? 2. A 15 volt battery is connected in parallel to two identical resistors. a) What is the voltage across R 1? 15 volts (use the loop rule) b) If R 1 and R 2 have different resistances, will they have different voltages? They will still both have a 15 V drop. 3. Two 30 Ω resistors are connected in parallel with a 10 volt battery. a) What is the total resistance of the circuit? b) What is the voltage drop across each resistor? c) What is the current flow through each resistor? 3. Two 30 Ω resistors are connected in parallel with a 10 volt battery. a) What is the total resistance of the circuit? 15 ohms 3. Two 30 Ω resistors are connected in parallel with a 10 volt battery. a) What is the total resistance of the circuit? 15 ohms b) What is the voltage drop across each resistor? c) What is the current flow through each resistor? b) What is the voltage drop across each resistor? 10 volts Each resistor is in its own loop with the 10 V battery, so each resistor has a voltage drop of 10 V. c) What is the current flow through each resistor? 8
9 3. Two 30 Ω resistors are connected in parallel with a 10 volt battery. a) What is the total resistance of the circuit? 15 ohms 4. Two 5.0 Ω resistors are connected in series with a 30 volt battery. a) What is the total resistance of the circuit? b) What is the voltage drop across each resistor? 10 volts Each resistor is in its own loop with the 10 V battery, so each resistor has a voltage drop of 10 V. c) What is the current flow through each resistor? 0.33 amps b) What is the current flow through each resistor? c) What is the voltage drop across each resistor? 4. Two 5.0 Ω resistors are connected in series with a 30 volt battery. a) What is the total resistance of the circuit? 10 ohms 4. Two 5.0 Ω resistors are connected in series with a 30 volt battery. a) What is the total resistance of the circuit? 10 ohms b) What is the current flow through each resistor? c) What is the voltage drop across each resistor? b) What is the current flow through each resistor? 3.0 amps The circuit has only one branch, so current flow is the same everywhere in the circuit. c) What is the voltage drop across each resistor? 4. Two 5.0 Ω resistors are connected in series with a 30 volt battery. a) What is the total resistance of the circuit? 10 ohms b) What is the current flow through each resistor? 3.0 amps The circuit has only one branch, so current flow is the same everywhere in the circuit. c) What is the voltage drop across each resistor? 15 volts Use the loop rule: 9
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