Circuit Problems Lecture

Introduction

• Presenter: Iman
• Focus: Solving problems related to circuit chapter

Problem 1: Charge in Defibrillator

• Question: A defibrillator passes 15 amperes through a patient's body for 0.1 seconds. Calculate the charge.
• Concept: Electrical current as charge flow (Q) over time (ΔT).
• Formula: ( I = \frac{Q}{ΔT} )
• Solution:
  • Rearrange to ( Q = I \times ΔT )
  • ( Q = 15 A \times 0.1 s = 1.5 C )
• Answer: 1.5 Coulombs (Choice B)

Problem 2: Potential Difference in Circuit

• Question: Two micro coulomb charge flows in a circuit loop. What is the total potential difference?
• Concept: Kirchhoff's Loop Rule: Total potential difference in a closed loop is 0 volts.
• Solution: The potential difference is 0 volts since the charge returns to its starting point.
• Answer: 0 volts

Problem 3: Resistance Ratio

• Question: Two conductors’ resistances are in 1:2 ratio. What is the resistivity ratio?
• Concept: Resistance formula: ( R = \rho \frac{L}{A} )
• Solution: Direct proportionality between resistance and resistivity.
  • If resistances are 1:2, resistivities must also be 1:2.
• Answer: 1:2 Ratio (Choice B)

Problem 4: EMF of a Battery

• Question: A voltaic cell with a 3 Ohm resistor and 0.1 Ohm internal resistance. What is the EMF?
• Concept: EMF is the voltage across the terminals with no current.
• Solution:
  • Calculate voltage with current: ( 0.5 A \times 3 \Omega = 1.5 V )
  • Adjust for internal resistance: ( EMF = V + IR = 1.5 V + (0.5 A \times 0.1 \Omega) = 1.55 V )
• Answer: 1.55 volts (Choice D)

Problem 5: Transformer Voltage and Current

• Question: Transformer output is 300% of input voltage. Find the current ratio.
• Concept: Power conservation: ( P_{in} = P_{out} )
• Solution:
  • Power definition: ( P = IV )
  • If voltage increases by 300%, current decreases to maintain equality.
  • Current out is 1/3 of current in.
• Answer: 1 to 3 Ratio (Choice A)

Problem 6: Circuit Resistance Calculation

• Question: Calculate total resistance with given resistors.
• Concept: Simplify circuit using series and parallel calculations.
• Solution:
  • Parallel: ( R_{3+4} = 16 ) ohms
  • Series with ( R_2: 4 + 16 = 20 ) ohms
  • Total: 3 resistances in parallel (20, 20, 20)
  • Calculate: ( R_{total} = 6.7 ) ohms
• Answer: 6.7 ohms (Choice B)

Problem 7: Moles of Electrons in Circuit

• Question: Calculate moles of electrons in a circuit over 10 seconds.
• Concept: Use charge and Faraday constant to find moles.
• Solution:
  • Charge: ( Q = V \times t / R = 500 C )
  • Convert to moles using Faraday constant.
  • Result: 5 x 10^-3 moles
• Answer: 0.005 moles (Choice A)

Problem 8: Voltage Drop Across Resistor

• Question: Calculate voltage drop across a specific resistor.
• Solution:
  • Use parallel resistance formula to simplify.
  • Total resistance = 1 ohm
  • Calculate current: ( I = 10 A )
• Answer: 10 amperes

Problem 9: Capacitance Change

• Question: Effect of doubling area and halving distance on capacitance.
• Concept: Capacitance formula ( C = \frac{\varepsilon A}{d} )
• Solution:
  • Doubling area and halving distance increases capacitance by factor of 4.
• Answer: 4 times (Choice D)

Problem 10: Charge on Capacitor

• Question: Calculate charge with given energy and voltage.
• Concept: Use charge-capacitance relation ( Q = CV ).
• Solution:
  • Substitute capacitance from energy formula.
  • Result: 0.1 Coulombs
• Answer: 0.1 Coulombs (Choice C)

Problem 11: Energy Dissipated by Resistor

• Question: Calculate energy dissipated over 5 seconds.
• Concept: Power and energy relation ( E = P \times ΔT )
• Solution:
  • Use power formula ( P = I^2 R )
  • Energy: 120 Joules
• Answer: 120 Joules (Choice C)

Problem 12: Current Direction and Magnitude

• Question: Find current between P and X.
• Concept: Kirchhoff's Junction Rule.
• Solution:
  • Balance in and out current at junction.
  • Current from P to X is 2 amperes.
• Answer: 2 amperes, away from P (Choice A)

Problem 13: Increasing Electric Field in Capacitor

• Question: What increases the electric field?
• Concept: Electric field equation ( E = \frac{V}{d} )
• Solution:
  • Adding a battery increases voltage and thus electric field.
• Answer: Adding an extra battery (Choice D)

Problem 14: Circuit Resistance

• Question: Calculate overall resistance in a circuit.
• Solution:
  • Series resistors: 12 ohms
  • Combined with parallel: 3 ohms total
• Answer: 3 ohms (Choice D)

Problem 15: Characterizing Ideal Meters

• Question: Characteristics of ideal voltmeters and ammeters.
• Solution:
  • Voltmeters: Infinite resistance
  • Ammeters: No resistance
• Answer: Voltmeter has infinite resistance, ammeter has no resistance (Choice C)

Conclusion

• Review and understand the concepts of electrical circuits and problem-solving techniques.
• Master use of Kirchhoff's rules, Ohm's Law, and the formulas relevant to circuits.