Two resistors of resistances R1 = 50 ± 3 ohm and R2 = 100 ± 4 ohm are connected in series. Find the equivalent resistance in series?

The correct answer is 150 ± 7 ohm.

Key Points

• When resistors are connected in series, their equivalent resistance is the sum of their individual resistances.
• Given resistances are R1 = 50 ± 3 ohms and R2 = 100 ± 4 ohms.
• The equivalent resistance (R_eq) in series is calculated as R1 + R2 = 50 + 100 = 150 ohms.
• The total uncertainty in equivalent resistance is the sum of the uncertainties of individual resistances.
• Uncertainty in equivalent resistance = ± (3 + 4) ohms = ± 7 ohms.

Additional Information

• Series Circuit
  • In a series circuit, the current passing through each component is the same.
  • Resistances add up when connected in series, which increases the overall resistance of the circuit.
• Uncertainty in Measurements
  • Uncertainty represents the range within which the true value is expected to lie.
  • It is crucial for indicating the precision of measurements and calculations.
• Ohm's Law
  • Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points.
  • It is represented as V = IR, where V is the voltage, I is the current, and R is the resistance.
• Resistors in Parallel
  • For resistors connected in parallel, the reciprocal of the equivalent resistance is the sum of the reciprocals of the individual resistances.
  • This configuration decreases the overall resistance of the circuit.