In an electrical circuit, five identical bulbs are connected in parallel to each other to a battery of 20 V (negligible internal resistance). When all the five bulbs glow, a current of 5 A is recorded. Then the power dissipated in the circuit and the resistance of each bulb are __________ and ________ respectively.

The correct answer is 100 W, 20 Ω.

Key Points

• Given in the question:
  • Potential difference across the circuit (V) = 20 V
  • Current in the circuit (I) = 5A
  • Using the formula P = V x I,
  • P = 20V x 5A = 100 W
  • Thus, the power dissipated in the circuit is 100 W.
  • Now, using Ohm's Law, R_net = V / I , we get,
  • Rnet = 20/5 = 4 Ω
  • This gives us the net resistance across the circuit.
  • As, it is given that the bulb are identical, their resistance will be same (say R).
  • Since the bulbs are connected in parallel combination,
  • 1/R_net = 1/R + 1/R +1/R + 1/R + 1/R
  • 1/R_net = 5/R
  • 1/4 = 5/R (as Rnet = 4 Ω)
  • R = 5 x 4
  • R = 20 Ω
  • Thus, the resistance of each bulb is 20 Ω.
• Therefore, the power dissipated in the circuit and the resistance of each bulb are 100W and 20 Ω respectively.

Additional Information

• Ohm's Law:
  • Ohm's law states that the electric current flowing through a conductor is directly proportional to the potential difference across its ends, provided the physical state of the conductor remains unchanged.
  • If I be the current flowing through the conductor and V the potential difference across its ends, then \(V {\displaystyle \propto } I\)
  • Hence, V = I x R , where, R is the constant of proportionality termed as Resistance of the conductor.
• Power:
  • Energy is the word for the ability to perform tasks. Power is the energy used to complete a task in a given amount of time.
  • P is used to represent it.
• These three formulas are used to calculate power in any electrical circuit.
  • P = V x I
  • P = I² x R
  • P = V² / R
• Resistance:
  • The amount of obstruction to current passage in an electrical circuit is measured as resistance. Ohms, or the Greek letter omega (Ω), are used to measure resistance (R).
  • There are mainly two ways of combination of resistance:
    • Series Combination:
      • When two or more resistances are connected end to end and the same current passes through each one successively, they are said to be connected in series. In this instance, the sum of the individual resistances found in the series combination determines the equivalent or total resistance.
      • In terms of mathematics, the equivalent resistance (R) of any number of resistances connected in series (R1, R2, R3,...) is as follows:
      • R = R1 + R2 + R3 + …
    • Parallel Combination:
      • When two or more resistances are connected between two places and have distinct current directions, they are referred to as being in parallel connections. In these circuits, the current splits off and recombines at the point where the branches meet.
      • The equivalent resistance (R) of any number of parallel resistances (R1, R2, R3,...) can be found mathematically as follows:
      • 1/R = 1/R1 + 1/R2 + 1/R3 + …