Calculate the current flowing through 4Ω (CAB) for the circuit shown in fig, using Kirchhoff's law. Calculate the current flowing through 4Ω (CDE) for the circuit shown, using supe... Calculate the current flowing through 4Ω (CAB) for the circuit shown in fig, using Kirchhoff's law. Calculate the current flowing through 4Ω (CDE) for the circuit shown, using superposition theorem. Derive an expression for equivalent resistances in series and parallel. Draw and explain the block diagram of an elementary power system. Read more

Steps to Solve

1. Analyze the first circuit using Kirchhoff's laws

   Identify the currents in the circuit:

   • Let $I_1$ be the current through the 2 Ω resistor.
   • Let $I_2$ be the current through the 3 Ω resistor.
   • Let $I_0$ be the current through the 4 Ω resistor.

   Set up Kirchhoff's voltage law (KVL) equations around the loops.

   For the loop containing 24V and 10V: $$ 24V - 10V - I_1(2Ω) - I_2(3Ω) = 0 $$

   For the loop with the 4 Ω resistor: $$ -I_2(3Ω) + I_0(4Ω) + 10V = 0 $$

2. Solve the KVL equations

   Rearrange the equations to express them in terms of a single variable. Solve the first equation for one current and substitute into the second equation to find all currents.

3. Calculate the second circuit using superposition theorem

   Identify the individual branches with separate voltage sources (100V and 20V).

   First, consider the 100V source:

   • Calculate equivalent resistance when the 20V source is turned off (replaced by a short circuit).
   • Find current through this part.

   Then, consider the 20V source:

   • Repeat the process turning the 100V source into a short circuit.
   • Calculate the current through the 4Ω resistor.

   Finally, add the currents from both sources to get the total current through the 4Ω resistor.

4. Derive expressions for equivalent resistances

   For resistors in series: $$ R_{eq} = R_1 + R_2 + \ldots + R_n $$

   For resistors in parallel: $$ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \ldots + \frac{1}{R_n} $$

5. Draw and explain the block diagram of an elementary power system

   • Draw a simple block diagram showing:
     • Power source
     • Transformer
     • Transmission lines
     • Load
   • Explain the function of each block:
     • Power Source: Generates electrical energy.
     • Transformer: Steps up or steps down voltage.
     • Transmission Lines: Distributes power over distances.
     • Load: Consumes electrical energy.