The circuit element where the impressed voltage is always in phase with the resulting current is

1. Fundamentals of Electric Current and Ohm's Law (basic)

To understand electricity, we must first visualize the relationship between Electric Current (I), which is the flow of charge, and Potential Difference (V), which is the electrical 'pressure' or 'push' that makes that flow possible. Ohm’s Law provides the fundamental bridge between these two. It states that at a constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends (Science, Class X, Electricity, p.176). Mathematically, this is expressed as V = IR, where R is the Resistance of the conductor.

Resistance is the property of a material to oppose the flow of current. The SI unit for resistance is the ohm (Ω). We define 1 ohm as the resistance of a conductor such that when a potential difference of 1 Volt is applied across it, a current of 1 Ampere flows through it (Science, Class X, Electricity, p.176). If you plot a graph of Voltage (V) against Current (I) for a standard resistor, you will get a straight line passing through the origin, indicating a linear relationship (Science, Class X, Electricity, p.193). This tells us that if you double the voltage, the current will also double, provided the resistance remains unchanged.

In more advanced applications, particularly in Alternating Current (AC) circuits, the behavior of a resistor is unique compared to other components like inductors or capacitors. In a purely resistive circuit, the voltage and current are always in phase. This means they reach their maximum and minimum values at the exact same moment. While other components cause 'lags' or 'leads' in current, an ideal resistor maintains a zero-degree phase difference, staying perfectly in sync with the impressed voltage.

Sources: Science, Class X (NCERT 2025 ed.), Electricity, p.176; Science, Class X (NCERT 2025 ed.), Electricity, p.193; Science, Class X (NCERT 2025 ed.), Electricity, p.189

2. Direct Current (DC) vs. Alternating Current (AC) (basic)

At its simplest level, Electric Current is the flow of charge. However, the way that charge flows determines whether we call it Direct Current (DC) or Alternating Current (AC). Think of DC as a one-way street where traffic moves steadily in a single direction, whereas AC is like a pendulum, where the flow of charge constantly reverses direction at a specific frequency (usually 50Hz or 60Hz depending on the country).

Direct Current (DC) is the standard for battery-operated devices and modern electronics. For instance, solar photovoltaic cells naturally produce DC. However, for large-scale utility use, this DC is often converted into AC using devices called inverters Environment, Shankar IAS Academy, Renewable Energy, p.288. On the other hand, Alternating Current (AC) is the backbone of our national power grid. The primary reason we use AC for our homes is efficiency: AC voltage can be easily "stepped up" or "stepped down" using transformers, allowing electricity to travel hundreds of kilometers with minimal energy loss.

A crucial nuance in AC circuits is the Phase Relationship between voltage (the pressure) and current (the flow). In a purely resistive circuit, such as a simple heating element or an ideal resistor, the voltage and current are perfectly in phase—they reach their peaks and zero-points at the exact same time. However, things change when we introduce "reactive" components like inductors (coils) or capacitors. These components cause a timing delay, or phase shift. In an inductor, the voltage "leads" the current, while in a capacitor, the current "leads" the voltage. Understanding these shifts is vital for managing the efficiency of the massive thermal power stations that dot the Indian landscape Geography of India, Majid Husain, Energy Resources, p.24.

Sources: Environment, Shankar IAS Academy, Renewable Energy, p.288; Geography of India, Majid Husain, Energy Resources, p.24

3. Electromagnetic Induction and Lenz's Law (intermediate)

In our previous steps, we saw how an electric current creates a magnetic field. Electromagnetic Induction (EMI) is essentially the reverse process: it is the phenomenon of generating an electric current in a circuit by changing the magnetic field linked with it. As noted in Science, Class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.195, electricity and magnetism are deeply linked; if a current-carrying wire behaves like a magnet, then a moving magnet should be able to "induce" electricity. This discovery by Michael Faraday changed the world, as it is the fundamental principle behind electric generators and transformers.

To induce a current, there must be relative motion between a conductor (like a copper coil) and a magnetic field. This can happen by moving a magnet toward a coil, moving the coil toward a magnet, or even by changing the strength of the magnetic field itself. The amount of "magnetic influence" passing through the loop is called Magnetic Flux (Φ). When this flux changes over time, an Electromotive Force (EMF) or voltage is produced. If the circuit is closed, this voltage drives an induced current. We can determine the direction of this induced current using Fleming’s Right-Hand Rule Science, Class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.207.

However, the most profound part of this concept is Lenz’s Law. It states that the direction of the induced current is always such that it opposes the change that produced it. Think of it as "nature’s inertia." If you try to push a North pole into a coil, the coil will induce a current that creates its own North pole to push back against you. This isn't just a quirk of physics; it is a requirement for the Conservation of Energy. If the coil attracted the magnet instead of repelling it, the magnet would accelerate indefinitely, creating infinite energy from nothing!

Sources: Science, Class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.195; Science, Class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.207

4. Principles of Transformers and Mutual Induction (intermediate)

At the heart of modern power distribution lies the principle of Mutual Induction. Imagine two coils of wire placed near each other but not touching. When an alternating current (AC) flows through the first coil (the primary), it creates a magnetic field that grows and collapses rhythmically. This changing magnetic flux passes through the second coil (the secondary), inducing a voltage across it. This is the essence of a Transformer: it transfers electrical energy from one circuit to another through a magnetic medium, without any direct physical connection.

Transformers are classified based on their winding ratio. If the secondary coil has more turns than the primary, it is a Step-up transformer (increasing voltage); if it has fewer, it is a Step-down transformer. While we often perform calculations using the concept of an ideal transformer—where no energy is lost—it is vital to remember that these are conceptual benchmarks. Just as political systems strive for democratic ideals that are often difficult to fully realize in practice Exploring Society: India and Beyond, Social Science-Class VII, From the Rulers to the Ruled: Types of Governments, p.192, real-world transformers face energy losses due to resistance in the wires and heat generated in the core.

One of the most critical nuances in AC circuits is the phase relationship between voltage (V) and current (I). In a purely resistive circuit, such as a simple electric lamp or a standard conductor, Ohm’s law (V = IR) dictates that the voltage and current are perfectly in phase—they peak and dip at the exact same moment Science, class X (NCERT 2025 ed.), Electricity, p.189. However, because a transformer is fundamentally inductive, it introduces a phase shift. In an ideal inductor, the voltage actually leads the current by 90 degrees. Understanding these shifts is essential for engineers calculating power efficiency in the national grid.

Sources: Science, class X (NCERT 2025 ed.), Electricity, p.189; Science, class X (NCERT 2025 ed.), Electricity, p.185; Exploring Society: India and Beyond, Social Science-Class VII, From the Rulers to the Ruled: Types of Governments, p.192

5. Household Electricity and Heating Effects (intermediate)

When an electric current flows through a conductor, the chemical energy of the battery or the mechanical energy of a generator is converted into electrical energy, which in turn manifests as heat due to the collisions of electrons with the atoms of the conductor. This is known as the heating effect of electric current. According to Joule’s Law of Heating, the heat (H) produced in a resistor is directly proportional to the square of the current (I²), the resistance (R), and the time (t) for which the current flows: H = I²Rt Science, class X (NCERT 2025 ed.), Electricity, p.189. In household circuits, where the voltage (V) is typically constant (e.g., 220V in India), we often calculate the heat using current derived from Ohm’s law (I = V/R).

This heating effect is both a challenge and a utility. While it causes undesirable energy loss in transmission wires, it is purposefully harnessed in appliances like electric irons, toasters, and heaters. In an incandescent bulb, the filament is designed to retain as much heat as possible so that it reaches a high enough temperature to emit light Science, class X (NCERT 2025 ed.), Electricity, p.190. To protect these circuits from the dangers of excessive heat—which can lead to fires via overloading or short-circuiting—a fuse is used. A fuse is a safety device made of a metal or alloy with an appropriate melting point; when current exceeds a safe limit, the fuse wire melts and breaks the circuit Science, class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.206.

In the context of Alternating Current (AC) used in our homes, the relationship between voltage and current depends on the type of appliance. Most heating devices are purely resistive. In such devices, the current is directly proportional to the voltage at every instant, meaning they are in phase—they reach their maximum and minimum values at the exact same time. This is distinct from reactive components like motors (inductive) or certain electronics (capacitive), where a phase shift occurs. In an ideal inductor, voltage leads the current, while in a capacitor, current leads the voltage. Therefore, only in a resistive heating element do we see a zero-degree phase difference between the impressed voltage and the resulting current.

Sources: Science, class X (NCERT 2025 ed.), Electricity, p.189; Science, class X (NCERT 2025 ed.), Electricity, p.190; Science, class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.206

6. Phase and Phasor Diagrams in AC Circuits (intermediate)

In our previous discussions, we looked at how current flows through resistors and how magnetic fields interact with circuits. However, in Alternating Current (AC) circuits, things get a bit more rhythmic. Unlike Direct Current (DC), where the voltage and current are constant, AC involves quantities that oscillate like waves. Because these waves (sine waves) change over time, their relative timing becomes crucial. This timing relationship is what we call Phase.

Imagine two swings moving back and forth. If they reach the highest point at the exact same moment, they are "in phase." If one reaches the peak while the other is still at the bottom, they are "out of phase." In an AC circuit, the Phase Angle (Φ) tells us the degree to which the current (I) leads or lags behind the voltage (V). To visualize this easily, engineers use Phasors—rotating vectors where the length represents the peak value and the angle represents the phase.

While a simple resistor maintains a zero-degree phase difference, real-world components like motors or transformers (which are inductive) shift these waves Science, Class X, Magnetic Effects of Electric Current, p.205. Understanding these shifts is vital because it determines the "Power Factor" of an appliance—essentially how efficiently it uses the electricity provided.

Sources: Science, Class X (NCERT 2025 ed.), Electricity, p.185; Science, Class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.205

7. Behavior of Passive Elements (L, C, R) in AC (exam-level)

When we deal with Alternating Current (AC), the behavior of circuit elements becomes more dynamic than in Direct Current (DC). In DC, we primarily focus on Resistance (R), where current flow depends directly on the potential difference across the ends Science, Class X, Electricity, p.181. However, in AC, the voltage and current are constantly changing direction and magnitude. This introduces the concept of phase—the timing relationship between when the voltage peaks and when the current peaks.

An ideal Resistor (R) is the simplest case. It follows Ohm's Law ($V = IR$) instantaneously at every moment. Because there is no "storage" of energy, the voltage and current are in phase. This means they reach their maximum, minimum, and zero points at exactly the same time. If you were to draw their waveforms, they would perfectly overlap in terms of their timing, even if their amplitudes differ Science, Class X, Electricity, p.184.

In contrast, reactive elements like inductors and capacitors cause a "lag" or "lead" because they store energy in magnetic and electric fields, respectively. An Inductor (L) (like a copper coil) opposes changes in current; this opposition causes the current to lag behind the voltage by 90 degrees. Conversely, a Capacitor (C) stores charge; the current flows most rapidly when the capacitor is empty, meaning the current peaks before the voltage across the plates has time to build up. Thus, in a capacitor, current leads the voltage by 90 degrees.

Sources: Science, Class X (NCERT 2025 ed.), Electricity, p.181; Science, Class X (NCERT 2025 ed.), Electricity, p.184

8. Solving the Original PYQ (exam-level)

Now that you have mastered the behavior of passive components in AC circuits, this question tests your ability to synthesize the concept of phase angle with physical circuit behavior. In your recent lessons, you learned that while resistance opposes current flow directly, reactance (found in capacitors and inductors) introduces a time delay. This question serves as a foundational check: it asks you to identify the specific impedance characteristic where the imaginary component is zero, meaning the power factor is unity. This is a classic example of how Basic Electrical Engineering principles are tested in competitive exams—by stripping away complexity to see if you understand the fundamental relationship between voltage and current waveforms.

To arrive at the correct answer, think through the phasor representation of each element. For An ideal resistor, the relationship is governed by the simplest form of Ohm’s Law, $V = IR$, where there is no frequency-dependent lag or lead. Because a resistor only dissipates energy and does not store it in a magnetic or electric field, the current peaks at the exact same moment as the voltage. As your coach, I recommend visualizing the sine waves: they cross the zero-axis simultaneously. Therefore, the phase difference is zero, making An ideal resistor the only element where the impressed voltage is always in phase with the resulting current.

UPSC frequently uses "ideal" reactive components as traps to see if you confuse "perfection" with "in-phase" behavior. In an ideal capacitor, the current leads the voltage by 90 degrees (recall the ICE mnemonic), while in an ideal coil (inductor), the voltage leads the current by 90 degrees (recall ELI). The ideal transformer is a particularly clever distractor; because it operates on the principle of mutual induction via magnetic flux, it is inherently inductive and involves phase shifts or even a 180-degree inversion between primary and secondary. Do not fall for the trap of thinking an "ideal" device must have zero shift; "ideal" simply means the component follows its theoretical phase-shifting laws without any internal resistance losses.