A cell of internal resistance 5Ω is connected to a resistor of 3Ω. Find the current flowing through the resistor if the e.m.f. of the battery is 1.2V.

The internal resistance ($r$) and the external resistance ($R$) are in series.

Ohm's Law states that $V = IR$, where $V$ is the e.m.f., $I$ is the current, and $R$ is the total resistance.

The correct option is (a).

2. What is the resistivity of a wire of length $5\text{cm}$ and cross sectional area of $0.2\text{m}^2$ if it offers a resistance of $10\Omega$ to the flow of current?

The resistance $R$ of a wire is given by $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity, $L$ is the length, and $A$ is the cross-sectional area.
Rearrange the formula to solve for resistivity $\rho$:

The correct option is (b).

3. A heating filament with p.d. of $20\text{V}$ across its ends has a current of $2\text{A}$ flowing through it for 3 seconds. Determine the heat energy generated in the filament if 80 percent of the electrical energy produced is converted to heat.

The electrical energy ($E$) produced is given by $E = VIt$, where $V$ is the potential difference, $I$ is the current, and $t$ is the time.

Only $80\%$ of the electrical energy is converted to heat.

The correct option is (d).

4. If the current flowing through a conductor is doubled and the resistance is constant, the power consumed by the conductor will increase to ..... times the original amount.

Power ($P$) consumed by a conductor is given by $P = I^2R$, where $I$ is the current and $R$ is the resistance.

Let the original current be $I_1$ and the original power be $P_1$.

If the current is doubled, the new current $I_2 = 2I_1$. The resistance $R$ remains constant.
The new power $P_2$ will be:

Since $P_1 = I_1^2 R$, we have:

The power consumed will increase to 4 times the original amount.
The correct option is (b).

5. In a series circuit with two resistors of equal value and a total current flow of $12\text{A}$, the current through each resistor is ............

In a series circuit, the current is the same at every point. This means the current flowing through each component (including each resistor) is equal to the total current flowing through the circuit.

Given that the total current flow is $12\text{A}$, the current through each resistor in the series circuit will also be $12\text{A}$. The fact that there are two resistors of equal value is relevant for calculating voltage drops or total resistance, but not for the current through individual components in a series circuit.
The question does not provide options that include $12\text{A}$. This suggests there might be a misunderstanding in the question or the provided options. However, based on the principles of series circuits, the current through each resistor must be the same as the total current. If this were a parallel circuit, the current would divide. Since it's explicitly stated as a series circuit, the current is constant.

Given the options (a) $6\text{A}$ and (b) $5\text{A}$, neither is $12\text{A}$. If the question intended to ask about a parallel circuit where the total current of $12\text{A}$ splits equally between two identical resistors, then the current through each would be $6\text{A}$. However, the question clearly states "series circuit".

Assuming there might be a typo in the question and it meant to ask for current in a parallel circuit with two identical resistors and a total current of $12\text{A}$:
If it were a parallel circuit with two equal resistors, the total current would split equally between them.

If we strictly follow the question as written (series circuit), the answer should be $12\text{A}$. Since $12\text{A}$ is not an option, and $6\text{A}$ is an option, it's highly probable the question implicitly assumes a parallel circuit or has a typo. Given the options, $6\text{A}$ is the most plausible intended answer if the question meant to imply current division.

Let's assume the question intended to ask about a parallel circuit, as $6\text{A}$ is an option.
In a parallel circuit, if two resistors are of equal value, the total current divides equally between them.

The correct option would be (a) under this assumption.

However, if we strictly adhere to the "series circuit" statement:
In a series circuit, the current is the same through all components.
Therefore, the current through each resistor would be $12\text{A}$. Since $12\text{A}$ is not an option, there is an inconsistency. I will proceed with the assumption that the question implies a scenario where the current divides, which would be a parallel circuit, given the options.

Assuming the question implies a parallel circuit for the options to make sense: