ROUTERA

Current Electricity

Class 12th Physics Chapter Case Study

Case Study 1: Ohm’s Law and Resistance

Ohm’s Law states that the current I flowing through a conductor between two points is directly proportional to the voltage V across the two points. This relationship is mathematically expressed as:

\(\ V=IR\)

where R is the resistance. Resistance depends on the material, length, and cross-sectional area of the conductor.

Questions:

  1. According to Ohm's Law, if the voltage across a conductor is doubled, the current will:
    • a) Double
    • b) Quadruple
    • c) Halve
    • d) Remain the same
  2. Resistance is influenced by which of the following factors?
    • a) Length of the conductor
    • b) Cross-sectional area
    • c) Material of the conductor
    • d) All of the above
  3. If a conductor has a resistance of 10 Ω and the current through it is 2 A, what is the voltage across it?
    • a) 5 V
    • b) 10 V
    • c) 20 V
    • d) 50 V
  4. What is the SI unit of resistance?
    • a) Volt
    • b) Ampere
    • c) Ohm
    • d) Watt

Answers:

  1. a) Double
  2. d) All of the above
  3. c) 20 V
  4. c) Ohm

Case Study 2: Series and Parallel Circuits

In a series circuit, components are connected end-to-end, so the same current flows through each component. The total resistance \(\ R_t \)​ in a series circuit is the sum of individual resistances:

\(\ Rt = R_1 + R_2 + R_3 + \ldots \)

In a parallel circuit, components are connected across the same two points. The total resistance \(\ R_t \)​ in a parallel circuit is given by:

\(\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots \)

Questions:

  1. In a series circuit, the total current is:
    • a) The same through all components
    • b) Different through each component
    • c) Zero
    • d) Dependent on the voltage
  2. In a parallel circuit, the voltage across each component is:
    • a) The same
    • b) Different
    • c) Zero
    • d) Depends on the resistance
  3. If two resistors of 4 Ω and 6 Ω are connected in series, what is the total resistance?
    • a) 2 Ω
    • b) 4 Ω
    • c) 6 Ω
    • d) 10 Ω
  4. For two resistors connected in parallel, if one has a resistance of 3 Ω and the other 6 Ω, the total resistance is:
    • a) 2 Ω
    • b) 4 Ω
    • c) 1.5 Ω
    • d) 9 Ω

Answers:

  1. a) The same through all components
  2. a) The same
  3. d) 10 Ω
  4. b) 2 Ω

Case Study 3: Kirchhoff’s Laws

Kirchhoff’s laws are two rules that deal with current and voltage in electrical circuits. Kirchhoff's Current Law (KCL) states that the total current entering a junction equals the total current leaving the junction. Kirchhoff's Voltage Law (KVL) states that the sum of the electrical potential differences (voltage) around any closed circuit is zero.

Questions:

  1. According to Kirchhoff's Current Law, at any junction:
    • a) Current can be lost
    • b) Current is conserved
    • c) Voltage is conserved
    • d) Resistance is constant
  2. In a closed circuit, Kirchhoff’s Voltage Law implies that:
    • a) Voltage can be gained
    • b) Voltage can be lost
    • c) The total voltage around the loop is zero
    • d) The voltage across resistors is constant
  3. If three currents entering a junction are 5 A, 3 A, and 2 A, what is the current leaving the junction?
    • a) 2 A
    • b) 3 A
    • c) 5 A
    • d) 10 A
  4. When applying Kirchhoff's Voltage Law in a circuit loop, the voltage across resistors is considered:
    • a) Positive
    • b) Negative
    • c) Zero
    • d) Constant

Answers:

  1. b) Current is conserved
  2. c) The total voltage around the loop is zero
  3. d) 10 A
  4. b) Negative

Case Study 4: Electric Power and Joule’s Law

The electric power PPP consumed in a circuit can be expressed in various forms:

\(\ P= IV = I^2R = \frac{V^2}{R}\)​

where I is the current, V is the voltage, and R is the resistance. Joule’s Law states that the heat produced in a conductor is proportional to the square of the current, the resistance, and the time the current flows:

\(\ Q = I^2Rt \)

Questions:

  1. The formula \(\ P=IV \) represents:
    • a) The relationship between power, current, and voltage
    • b) The relationship between resistance and voltage
    • c) The relationship between heat and time
    • d) None of the above
  2. If the current through a resistor is doubled, the power consumed will increase by a factor of:
    • a) 2
    • b) 4
    • c) 6
    • d) 8
  3. The unit of electric power is:
    • a) Watt
    • b) Joule
    • c) Ampere
    • d) Volt
  4. According to Joule’s Law, the heat produced in a resistor is:
    • a) Directly proportional to the voltage
    • b) Directly proportional to the resistance and time
    • c) Inversely proportional to the current
    • d) Both b and c

Answers:

  1. a) The relationship between power, current, and voltage
  2. b) 4
  3. a) Watt
  4. d) Both b and c

Case Study 5: Series and Parallel Capacitors in Circuits

Capacitors can be connected in series and parallel just like resistors. The total capacitance for capacitors in series is given by:

\(\frac{1}{C_t} = \frac{1}{C_1} + \frac{1}{C_2} + \ldots\)

And for capacitors in parallel, the total capacitance is:

\(\ C_t= C_1 + C_2 + \ldots\)

Questions:

  1. In a series capacitor circuit, the total capacitance is:
    • a) Greater than the largest capacitance
    • b) Less than the smallest capacitance
    • c) The sum of individual capacitances
    • d) The product of individual capacitances
  2. In a parallel capacitor circuit, the voltage across each capacitor is:
    • a) The same
    • b) Different
    • c) Zero
    • d) Depends on the capacitance
  3. If two capacitors of 2 µF and 3 µF are connected in series, the total capacitance is:
    • a) 1 µF
    • b) 2 µF
    • c) 5 µF
    • d) 6 µF
  4. For two capacitors connected in parallel with capacitances of 4 µF and 6 µF, the total capacitance is:
    • a) 2 µF
    • b) 4 µF
    • c) 6 µF
    • d) 10 µF

Answers:

  1. b) Less than the smallest capacitance
  2. a) The same
  3. a) 1.2 µF
  4. d) 10 µF