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A number of resistors R1,R2,R3... are co...

A number of resistors `R_1,R_2,R_3`... are connected in series such that R, is the equivalent resistance of series combination. A current I is flowing in the circuit due to a potential V applied across the circuit. `V_1,V_2,V_3`.... are potential difference across `R_1,R_2,R_3`.... respectively. Choose the incorrect statement

A

Same current I will flow through each resistor

B

`V_1+V_2+V_3`+….=V

C

`V_1=(R_1/R_S)V, V_2=(R_2/R_S)V, V_3=(R_3/R_S)V`….

D

`V_1=(R_S/R_1)V, V_2=(R_S/V_2)V,V_3=(R_S/R_3)V`…..

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the statements related to resistors connected in series and determine which one is incorrect. ### Step-by-Step Solution: 1. **Understanding Series Resistors**: - When resistors \( R_1, R_2, R_3, \ldots \) are connected in series, the total or equivalent resistance \( R_s \) is given by: \[ R_s = R_1 + R_2 + R_3 + \ldots \] 2. **Current in Series Circuit**: - In a series circuit, the same current \( I \) flows through each resistor. Therefore, we can state: \[ I = I_1 = I_2 = I_3 = \ldots \] - This means that the current flowing through each resistor is identical. 3. **Voltage Across Each Resistor**: - The potential difference across each resistor can be calculated using Ohm's law: \[ V_1 = I \cdot R_1, \quad V_2 = I \cdot R_2, \quad V_3 = I \cdot R_3 \] - The total voltage \( V \) across the series circuit is the sum of the individual voltages: \[ V = V_1 + V_2 + V_3 + \ldots \] 4. **Using Kirchhoff's Voltage Law (KVL)**: - According to KVL, the sum of the potential differences in a closed loop is equal to the total voltage supplied. Thus: \[ V - V_1 - V_2 - V_3 - \ldots = 0 \implies V = V_1 + V_2 + V_3 + \ldots \] 5. **Identifying the Incorrect Statement**: - Based on the above analysis, we can evaluate the provided statements. - The correct statements are: - The current is the same through each resistor (True). - The total voltage is equal to the sum of the individual voltages (True). - The equivalent resistance is the sum of the individual resistances (True). - The incorrect statement would typically suggest a relationship that contradicts these principles, such as suggesting that the voltage across one resistor is somehow related to the equivalent resistance in a way that does not hold true. ### Conclusion: The incorrect statement is identified as option D (as per the video), which does not conform to the principles of series circuits.
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