Practice Questions

Compare the flow of current through two copper wires of the same length but with one having a cross-sectional area of $A$ and the other $2A$, when connected to the same voltage source.

Propose a suitable material for the heating element of an electric toaster and justify your choice based on two key electrical and thermal properties.

Evaluate the statement: 'In a series circuit, the resistor with the highest resistance consumes the most power.' Justify your conclusion.

Analyze what happens to the current in a circuit if the potential difference is kept constant, but the resistance is quadrupled.

Define electric current and state its SI unit.

Calculate the total electric charge that passes through a conductor in 5 minutes if a steady current of $200 \text{ mA}$ is flowing through it.

What is an electric circuit? List the essential components of a simple circuit.

State Ohm's law. Write the mathematical expression relating potential difference, current, and resistance.

Recall the formula for the equivalent resistance of resistors connected in series. Calculate the total resistance if three resistors of $2 \Omega$, $3 \Omega$, and $5 \Omega$ are connected in series.

Justify why alloys are generally more suitable than pure metals for making the coils of electric heating devices like toasters and irons.

What is the commercial unit of electrical energy? Express its value in joules.

List the factors on which the resistance of a conductor depends.

Describe how an ammeter and a voltmeter should be connected in a circuit. What does each instrument measure?

State Joule's law of heating. List the three factors that determine the heat produced in a resistor.

Define electric power and state its SI unit. Write three different formulas to express electric power.

An electric lamp draws a current of $0.4 \text{ A}$ when connected to a $220 \text{ V}$ source. Calculate the resistance of its filament. If the source voltage drops to $110 \text{ V}$, what current will the lamp draw, assuming the resistance remains constant?

Recall the formula for electric current in terms of charge and time. Calculate the charge that flows through a conductor if a current of $2$ A flows for $30$ seconds.

Explain the concept of electric potential difference and name its SI unit.

Define one ampere.

Explain why alloys like nichrome are used in heating devices such as electric toasters.

Contrast the physical quantities measured by the units Ampere and Coulomb.

Calculate the heat produced in joules when a current of $2 \text{ A}$ flows through a $5 \Omega$ resistor for $10$ seconds.

Examine why an electric fuse is rated in amperes (e.g., $5 \text{ A}$) and not in volts.

Justify the use of parallel circuits for domestic wiring as opposed to series circuits. Provide at least three distinct arguments to support your position.

Propose methods to connect four resistors of resistance $4 \Omega$, $8 \Omega$, $12 \Omega$, and $24 \Omega$ to obtain (a) the maximum possible equivalent resistance and (b) the minimum possible equivalent resistance. Justify your proposed arrangements and calculate both values.

Create a hypothetical scenario for a simple household circuit. The circuit is connected to a $220$ V source and contains a refrigerator rated $450$ W, a television rated $110$ W, and two lamps each rated $55$ W, all operating in parallel. Formulate the total current drawn from the mains and propose a suitable standard fuse rating for this circuit, justifying your choice.

Three resistors of resistance $5 \Omega$, $10 \Omega$, and $15 \Omega$ are connected in series to a $6 \text{ V}$ battery. Calculate: (a) the total resistance of the circuit, (b) the total current flowing through the circuit, and (c) the potential difference across the $10 \Omega$ resistor.

An electric motor connected to a $220 \text{ V}$ line draws a current of $5 \text{ A}$. Calculate the power of the motor and its resistance.

Calculate the work done in moving a charge of $5 \text{ C}$ from a point at a potential of $100 \text{ V}$ to a point at a potential of $120 \text{ V}$.

A wire of length $2 \text{ m}$ and cross-sectional area $1.7 \times 10^{-6} \text{ m}^2$ has a resistance of $2 \times 10^{-2} \Omega$. Calculate the resistivity of the material of the wire.

Design an experiment to verify Ohm's law for a metallic conductor. Your design must include a labeled circuit diagram, a list of required apparatus, the procedure to be followed, and how you would analyze the data to formulate a conclusion.

A student claims that a thicker wire will always have less resistance than a thinner wire. Critique this statement. Justify whether it is universally correct or under what specific conditions it holds true, using the formula for resistance.

An electric iron is rated at $1100$ W and is designed to operate on a $220$ V supply. A student suggests using a $5$ A fuse for its circuit. Evaluate this suggestion. Justify whether this fuse is an appropriate and safe choice.

Design a procedure to experimentally determine the electrical resistivity of an unknown metallic wire. List the essential apparatus required, the formula you would use, and the specific measurements you would need to take.

Justify the design principles that an ideal ammeter should have a very low resistance, while an ideal voltmeter should have a very high resistance. Relate your justification to how each instrument is connected in a circuit.

Design a circuit using three identical resistors, each with resistance $R$, to achieve a total equivalent resistance of $\frac{2}{3}R$. Draw the circuit diagram and provide a mathematical justification for your design.

Recall the formula for the equivalent resistance of resistors connected in parallel. Explain why the equivalent resistance in a parallel combination is always less than the smallest individual resistance.

Critique the practicality of a circuit design where a lamp with a resistance of $100 \Omega$ and a toaster with a resistance of $50 \Omega$ are connected in series to a $220$ V source. Evaluate their performance by calculating the power consumed by each appliance.

Two resistors, $R_1 = 30 \Omega$ and $R_2 = 60 \Omega$, are connected in parallel across a $12 \text{ V}$ battery. Calculate: (a) the total equivalent resistance of the circuit, (b) the total current drawn from the battery, and (c) the current flowing through each resistor.

You are given four resistors of $2 \Omega$, $4 \Omega$, $6 \Omega$, and $8 \Omega$. Create a circuit combination using all four resistors that results in a total equivalent resistance of $5 \Omega$. You must draw the circuit diagram and mathematically prove your design.

Two resistors, each of resistance $R$, are connected to the same voltage source $V$. In case 1, they are connected in series. In case 2, they are connected in parallel. Compare the power consumed in both cases and analyze which combination will produce more heat in the same amount of time.

Three resistors with resistances $R_1 = 2 \Omega$, $R_2 = 3 \Omega$, and $R_3 = 6 \Omega$ are available. Demonstrate how to connect them to obtain an equivalent resistance of $4 \Omega$. Then, calculate the total current if this combination is connected to a $12 \text{ V}$ battery.

You are given two wires, A and B, made of the same material and of equal length. Wire A has a diameter that is twice the diameter of wire B. Formulate the ratio of the heat produced in wire A to that in wire B ($H_A : H_B$) if they are connected in parallel to the same voltage source for the same amount of time.

What is electrical resistivity? State its SI unit.

An electric geyser rated $1500 \text{ W}$ is used for 2 hours daily. Calculate the cost of energy consumed by it in a 30-day month, if the rate per unit is Rs. $5.00$. (1 unit = $1 \text{ kWh}$).