Resistance

In the question, we have the values for external resistance, current, and voltage of the cell. As per ohm's law, these quantities are related to each other. Hence, ohm’s law will be used to calculate the internal resistanceof the cell through the values.

Formula used:

As per ohm’s law, V = I(R+r)

• Where V is voltage, 
• I is current, 
• R is external resistance 
• r is internal resistance.

Complete step-by-step solution:

Given: Internal resistance = 2.1V, Current = 0.2A, external resistance = 10Ω.

To calculate internal resistance, we will use ohm’s law.

V = I(R+r)

2.1 = (0.2)(10+r)

r = 0.5 Ω

Thus, the internal resistance of the given cell is 0.5Ω.

Hence, the correct option is (C).

Note: The sum of internal and external resistance is the total resistance. 

Diode Circuit Analysis

The diode D₁ will be in reverse bias, so it will block the current and diode D₂ will be in forward bias, so it will pass the current.

Current Calculation:

Given that the total resistance in the circuit is:

• Resistance of the first resistor = 2Ω
• Resistance of the second resistor = 2Ω
• Total resistance (R) = 2Ω + 2Ω = 4Ω

Using Ohm's law, the current i is:

i = V / R = 10V / 4Ω = 2.5A

Therefore, the current passing through the circuit is 2.5 A.

Joule's Law of Heating Calculation

We are given the following equation for :

The current is given by:

For , we solve for :

Using Joule's Law of Heating:

According to Joule's law of heating, the infinitesimal heat is given by:

To find the total heat , we integrate from to :

Expanding the integrand and integrating:

Substituting the limits:

Conclusion:

The total heat is given by .

To determine the effective resistance when the wires are connected in series, we need to first understand the difference in resistance calculation for parallel and series circuits.

Given: The effective resistance of a parallel connection of four wires is .

Let's denote the resistance of each wire as . In a parallel circuit, the total resistance is given by:

Since all wires have the same resistance , the equation becomes:

Given that , we can substitute:

Solving for :

This means each wire has a resistance of .

When these wires are connected in series, the total resistance is simply the sum of individual resistances:

Thus, the effective resistance when the wires are connected in series is .

Therefore, the correct answer is: .

When two resistors are connected in parallel, the voltage across each resistor is the same. The power dissipated as thermal energy in a resistor is given by the formula , where is the voltage across the resistor and is its resistance.

Let the resistors be and .

Since both resistors are in parallel, the voltage across both is the same. The power for the 100 resistor is:

And the power for the 200 resistor is:

The ratio of thermal energy (power) developed in the 100 resistor to that in the 200 resistor is:

Thus, the ratio of thermal energy developed in the 100 resistor to that in the 200 resistor is 2:1.