Which one among the following is the true representation of (i) variable DC potential (ii) rheostat and (Hi) AC ammeter respectively?

1. Electric Current and Basic Circuit Components (basic)

To understand electricity, we must first look at the electric circuit: a continuous and closed path through which electric current flows. Think of it as a circular track for electrons; if the track is broken at any point (like an open switch), the flow stops immediately. A basic circuit typically comprises a source of energy (like a cell), a conducting wire, and a component that uses the energy (like a bulb) Science, Class X (NCERT 2025 ed.), Chapter 11, p.174. While a single electric cell provides a small amount of energy, we often combine them to form a battery, where the positive terminal of one cell is connected to the negative terminal of the next to increase the total potential difference Science-Class VII, NCERT (Revised ed 2025), Electricity: Circuits and their Components, p.25.

Since drawing realistic pictures of every component is tedious, scientists use standardized circuit symbols. These symbols act as a universal language. For instance, a simple cell is shown by two parallel lines (one long for positive, one short and thick for negative). When we need to adjust the flow of current in a circuit without changing the voltage source, we use a rheostat (or variable resistor). In schematic diagrams, a rheostat is represented by a zig-zag line with an arrow crossing through it or pointing down toward it, signifying that its resistance value can be "slid" up or down Science, Class X (NCERT 2025 ed.), Chapter 11, p.175.

Furthermore, we often need to measure the electricity flowing through these paths. An ammeter is the device used to measure electric current. However, current comes in two flavors: Direct Current (DC) and Alternating Current (AC). To distinguish between them in a diagram, an AC ammeter is represented by a circle containing the letter 'A' with a small wave or tilde (~) symbol either inside or underneath it. This tilde is the standard shorthand for "alternating," indicating the current reverses direction periodically Science, Class X (NCERT 2025 ed.), Chapter 11, p.175.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.174-175; Science-Class VII, NCERT (Revised ed 2025), Electricity: Circuits and their Components, p.25

2. Electric Potential and DC Voltage Sources (basic)

To understand electricity, we must first understand what makes charges move. Imagine a water tank placed on a roof connected to a tap on the ground; water flows because of the pressure difference created by gravity. In a similar way, electrons in a conductor move only when there is a difference in electric pressure, which we formally call Electric Potential Difference.

By definition, the electric potential difference (V) between two points in a circuit is the work done (W) to move a unit charge (Q) from one point to the other. Mathematically, this is expressed as V = W/Q. The SI unit for this is the Volt (V), named after the physicist Alessandro Volta Science, Class X (NCERT 2025 ed.), Chapter 11, p.173. Think of one volt as the electrical "push" required to perform 1 Joule of work while moving 1 Coulomb of charge.

To maintain this flow of current, we use a DC Voltage Source, such as a dry cell or a battery. A chemical reaction within the cell generates a potential difference across its terminals even when no current is being drawn. When the cell is connected to a circuit, this potential difference forces charges into motion. In circuit diagrams, we represent these components using standardized symbols to ensure clarity:

Component	Description/Symbolic Logic
Standard Battery	Represented by a long vertical line (positive terminal) and a shorter, thicker line (negative terminal).
Variable DC Source	A battery symbol with a diagonal arrow across it, indicating that the voltage output can be adjusted.
Rheostat	A variable resistor (zig-zag line with an arrow) used to change the current without changing the voltage source itself.

In more complex setups, when resistors are connected in series, the total potential difference across the entire combination is simply the sum of the potential differences across each individual resistor (V = V₁ + V₂ + V₃) Science, Class X (NCERT 2025 ed.), Chapter 11, p.183. This additive nature is a fundamental principle used in designing electronics, from simple flashlights to complex power grids.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.173; Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.183

3. Resistance and Ohm's Law (basic)

At the heart of every electrical circuit is a fundamental relationship discovered by Georg Simon Ohm in 1827. Ohm’s Law states that the current (I) flowing through a metallic conductor is directly proportional to the potential difference (V) across its ends, provided its temperature and other physical conditions remain constant. Mathematically, this is expressed as V ∝ I, or more commonly, V = IR Science, Chapter 11: Electricity, p.176.

Resistance (R) is the proportionality constant in this equation. It represents the inherent property of a material to oppose the flow of electric charges. Think of it as "electrical friction." While a battery provides the push (voltage), the resistance determines how much current actually manages to get through. The SI unit for resistance is the ohm, denoted by the Greek letter Ω. If a potential difference of 1 Volt across a conductor produces a current of 1 Ampere, the resistance of that conductor is defined as 1 Ω Science, Chapter 11: Electricity, p.176.

In practical applications, we often need to control the amount of current without changing the voltage source. This is achieved using a variable resistor or rheostat. By manually increasing the resistance, we can decrease the current in the circuit, and vice versa. When we plot a graph of Potential Difference (V) on the y-axis against Current (I) on the x-axis, the result is a straight line passing through the origin, which confirms that the ratio V/I remains constant for a given conductor Science, Chapter 11: Electricity, p.193.

Scenario	Resistance Change	Current Change (at constant V)
Good Conductor (e.g., Copper)	Low Resistance	High Current
Insulator (e.g., Rubber)	Extremely High Resistance	Negligible Current

Sources: Science, Chapter 11: Electricity, p.176; Science, Chapter 11: Electricity, p.193

4. The Rheostat: Controlling Current Flow (intermediate)

In the study of electrical circuits, we often encounter situations where we need to vary the intensity of the current without altering the potential difference (voltage) of the power source. This is where the rheostat, also known as a variable resistance, becomes essential. According to Ohm’s Law (I = V/R), if the voltage (V) remains constant, the current (I) is inversely proportional to the resistance (R) Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.176. By manually adjusting the resistance using a rheostat, we can precisely control how much current flows through the circuit.

Physically, a rheostat typically consists of a long resistive wire wound around an insulating cylinder, with a sliding contact (or wiper) that moves along the length of the wire. As you move the slider, you change the effective length of the wire included in the circuit. Since resistance increases with the length of the conductor, increasing the length of the wire through the slider increases the total resistance, which subsequently reduces the current flowing through the circuit Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.176.

In technical schematic diagrams, a rheostat is represented by the standard zig-zag resistor symbol but with a diagonal arrow across it or a sliding contact arrow pointing toward it Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.175. This visual cue indicates that the resistance value is not fixed but can be adjusted by the user. While a standard resistor provides a stable, fixed resistance, the rheostat allows for dynamic control, making it a staple in laboratory experiments and various electrical gadgets where current regulation is required.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.175-176

5. Measuring Instruments: Ammeter and Voltmeter (intermediate)

To understand how we monitor and control electricity, we must look at two primary 'gauges': the Ammeter and the Voltmeter. Just as a water meter measures the flow of water through a pipe, an Ammeter measures the electric current (the rate of flow of electric charges) in a circuit. Because it needs to 'count' every charge passing through, it must be connected in series — meaning the current flows directly through the device Science, Class X (NCERT 2025 ed.), Chapter 11, p.172. To ensure it doesn't hinder the flow it is trying to measure, a good ammeter is designed with very low resistance.

In contrast, a Voltmeter measures the potential difference (the electrical 'pressure' or work done) between two specific points in a circuit. Think of it like measuring the height difference between two floors; you don't need to be part of the staircase, you just need to touch both levels. Therefore, a voltmeter is always connected in parallel across the component being measured Science, Class X (NCERT 2025 ed.), Chapter 11, p.173. To prevent current from 'leaking' into the meter and away from the main circuit, a voltmeter is built with very high resistance.

In schematic diagrams, these instruments are represented by circles with their respective unit initials: 'A' for Ammeter and 'V' for Voltmeter. If we are dealing with Alternating Current (AC), you will often see a small tilde symbol (~) inside or below the circle to distinguish it from a Direct Current (DC) instrument. We also use components like the rheostat (a variable resistor) to manually adjust the current in a circuit without changing the voltage source, which is typically shown as a zig-zag line with an arrow pointing through or at it Science, Class X (NCERT 2025 ed.), Chapter 11, p.175.

Feature	Ammeter	Voltmeter
Measures	Electric Current (I)	Potential Difference (V)
Connection	Series	Parallel
Ideal Resistance	Zero (Very Low)	Infinite (Very High)
Unit	Ampere (A)	Volt (V)

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.172, 173, 175

6. Alternating Current (AC) vs Direct Current (DC) Indicators (intermediate)

In the study of electrical circuits, standardization is our best friend. To communicate complex designs clearly, we use circuit diagrams—schematic representations where every component has a specific, universally recognized symbol. As noted in Science-Class VII, Electricity: Circuits and their Components, p.34, using these symbols makes it significantly easier to visualize and analyze how electricity flows through a system. When we move beyond simple batteries to more complex systems, we must distinguish between Direct Current (DC), which flows in one constant direction, and Alternating Current (AC), which periodically reverses its direction.

To identify the type of current or the adjustability of a component, we look for specific "modifiers" on the base symbols. For instance, a standard DC source is represented by parallel long and short lines (representing the positive and negative terminals), but if that source is variable (meaning you can change the voltage output), we draw a diagonal arrow across it. Similarly, a rheostat—a device used to control current by varying resistance—is represented by a zig-zag line with an arrow pointing to it, indicating its sliding contact nature. You can find these standard conventions detailed in Science, class X, Electricity, p.174.

The most critical indicator for Alternating Current (AC) is the tilde symbol (~). This wavy line mimics the sinusoidal wave shape of alternating current. In India, our household power supply is AC with a frequency of 50 Hz, meaning the current changes direction 100 times per second Science, class X, Magnetic Effects of Electric Current, p.206. Therefore, while a standard Ammeter is a circle with an 'A', an AC Ammeter will specifically feature that tilde (~) either inside or directly beneath the 'A' to warn the technician that the instrument is designed for fluctuating current rather than steady DC.

Component	Standard Symbol Base	AC/Variable Indicator
Ammeter	Circle with 'A'	Tilde (~) for AC; Straight line (—) for DC
Voltage Source	Parallel lines (Battery)	Diagonal arrow (↗) for Variable DC
Resistor	Zig-zag line	Arrow (↗) or sliding contact for Rheostat

Sources: Science-Class VII . NCERT(Revised ed 2025), Electricity: Circuits and their Components, p.34; Science , class X (NCERT 2025 ed.), Electricity, p.174; Science , class X (NCERT 2025 ed.), Magnetic Effects of Electric Current, p.206

7. Standardized Circuit Symbols (NCERT Standards) (exam-level)

In electrical engineering and physics, standardized symbols allow scientists and engineers globally to communicate complex circuit designs through schematic diagrams. A circuit diagram is a simplified representation of an electrical circuit using these conventional symbols rather than realistic pictures of the components Science, Class VII, Chapter 3, p.34. This standardization ensures that a circuit designed in India can be perfectly understood in any other part of the world. At the foundational level, we represent energy sources like the electric cell with two parallel lines: a longer, thin line representing the positive terminal and a shorter, thicker line for the negative terminal. When multiple cells are combined to increase voltage, they form a battery Science, Class X, Chapter 11, p.175. However, in advanced experiments, we often need a variable DC potential source (or variable voltage). This is symbolized by the standard battery icon with a diagonal arrow drawn across it, signifying that the output voltage can be adjusted. This is distinct from a rheostat (variable resistor), which uses a zig-zag line with an arrow to indicate that it controls the flow of current by varying resistance, rather than changing the source voltage itself. Measuring instruments also follow strict symbolic conventions. An Ammeter (which measures current) is represented by a circle with the letter 'A', while a Voltmeter (measuring potential difference) is a circle with 'V'. To distinguish between current types, a straight horizontal line (-) or the letters 'DC' indicates Direct Current, while a tilde symbol (~) is used to denote Alternating Current (AC). Therefore, an AC ammeter is marked with an 'A' accompanied by a tilde (~). Other critical symbols include Light Emitting Diodes (LEDs), which are shown as a triangle pointing in the direction of current flow with two small outward arrows representing the emission of light Science, Class VII, Chapter 3, p.34.

Component	Standard Symbol Description	Primary Function
Variable DC Source	Battery symbol with a diagonal arrow	Adjusts the input voltage of the circuit
Rheostat	Zig-zag line with a sliding contact arrow	Controls current by varying resistance
AC Ammeter	Circle with 'A' and a tilde (~)	Measures the magnitude of alternating current
Plug Key (Closed)	Bracket with a dot inside ( . )	Completes the circuit to allow current flow

Sources: Science, Class X (NCERT 2025 ed.), Chapter 11: Electricity, p.174-175; Science, Class VII (NCERT 2025 ed.), Chapter 3: Electricity: Circuits and their Components, p.34

8. Solving the Original PYQ (exam-level)

Now that you have mastered the fundamental properties of electricity, this question tests your ability to translate those abstract concepts into standardized schematic symbols. In the UPSC Preliminary Examination, precision is key. You have learned that variability in a circuit is denoted by a diagonal arrow and that the nature of the current—whether Direct Current (DC) or Alternating Current (AC)—is indicated by specific visual cues like parallel lines or tildes. This question synthesizes those building blocks into a single identification task based on Science, class X (NCERT 2025 ed.) > Chapter 11: Electricity.

To arrive at the correct answer, follow a step-by-step elimination process. First, identify the variable DC potential; it must feature the long and short parallel lines of a battery intersected by a diagonal arrow. Next, look for the rheostat, which is represented by a zig-zag resistor symbol equipped with either a diagonal arrow or a sliding contact to show adjustable resistance. Finally, the AC ammeter is characterized by a circle containing the letter 'A' with a small tilde (~) beneath it, signifying its capacity to measure alternating current. Option 1 correctly sequences these three symbols, matching each component to its technical representation.

A common trap in these questions is the omission of variability indicators. UPSC may present a fixed DC source or a fixed resistor to see if you overlook the necessary diagonal arrow. Another frequent distractor involves the distinction between DC and AC; a plain 'A' inside a circle represents a DC ammeter, and selecting it for an AC requirement is a classic error. By methodically checking for the arrow (for variability) and the tilde (for AC), you can confidently navigate through the distractors and secure the marks.