Grade 10th · Physics · Electricity
Complete NCERT step-by-step derivation of the equivalent resistance formula for resistors connected in series (Rs = R1 + R2 + R3) for Class 10 Physics. Includes circuit diagrams, Ohm's law proofs, and solved numerical problems.
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When two or more resistors are joined end-to-end consecutively, they are said to be connected in series. Two golden rules govern series circuits: 1. The same electric current (I) flows sequentially through every resistor. 2. The total potential difference (V) across the combination equals the sum of potential differences across individual resistors: V = V₁ + V₂ + V₃.
Step 1: Consider three resistors of resistance R₁, R₂, and R₃ connected in series across a battery of voltage V. Let the steady current flowing through the circuit be I. Step 2: According to the conservation of electric potential: V = V₁ + V₂ + V₃. Step 3: By Ohm's Law (V = I·R), the potential drop across each resistor is: V₁ = I·R₁, V₂ = I·R₂, and V₃ = I·R₃. Step 4: If R_s is the equivalent resistance of the entire series combination, the total voltage across the circuit is V = I·R_s. Step 5: Substitute these expressions into the voltage equation: I·R_s = I·R₁ + I·R₂ + I·R₃. Step 6: Factor out current (I) from both sides: I·R_s = I·(R₁ + R₂ + R₃). Dividing both sides by I gives: R_s = R₁ + R₂ + R₃. (Hence Proved).
1. The equivalent resistance (R_s) in a series combination is always GREATER than the highest individual resistance in the combination. 2. Adding more resistors in series increases the total circuit resistance and consequently decreases the total current. 3. Power dissipation is highest across the resistor with the greatest resistance (P = I²R).
In domestic wiring, series circuits are never used because: 1. If one appliance fails or is switched off, the entire circuit is broken and all other appliances stop working. 2. All appliances must share the same current, even though an electric heater needs 15A while a light bulb needs only 0.5A. 3. The voltage is divided among appliances, meaning each device receives less than the standard 220V required for optimal operation.
Always state the governing principle or formula first, write given values with standard SI units, substitute clearly, and highlight the final numerical answer with units in a box for full step marking.
Watch for unit prefixes (cm to m, minutes to seconds, g to kg, degrees to radians). In coordinate and ray optics problems, double-check Cartesian sign conventions before computing.
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Start with total voltage V = V₁ + V₂ + V₃. By Ohm's law, substitute V = I·R_s, V₁ = I·R₁, V₂ = I·R₂, and V₃ = I·R₃ to get I·R_s = I·R₁ + I·R₂ + I·R₃. Canceling I gives R_s = R₁ + R₂ + R₃.
According to the principle of conservation of electric charge, charge cannot accumulate at any point in a single unbranched wire. Since there is only one pathway for electrons to flow, the rate of charge flow (current I) must be identical through every component.
Using the series formula R_s = R₁ + R₂ + R₃ = 2Ω + 3Ω + 5Ω = 10Ω.