a battery supply a current of 2A through a 2 ohm resistor and a current of 1 a through 5ohm what is internal resistance of battery
a battery supply a current of 2A through a 2 ohm resistor and a current of 1 a through 5ohm what is internal resistance of battery
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Verified answer
Given :
Current flow in circuit when resistor of 2Ω connected to battery = 2A
Current flow in circuit when resistor of 5Ω connected to battery = 1A
To Find :
Internal resistance of the battery.
Solution :
■ As per ohm's law, current flow in circuit is directly proportional to the applied potential difference at constant temperature
Mathematically, V = I × R
Let internal resistance of the battery be r.
In this question, potential difference remains same across resistor in both cases.
❇ In the first case, a resistor of 2Ω is connected with a battery.
➠ V = I × (R₁ + r)
➠ V = 2 × (2 + r) __ (i)
❇ In the second case, a resistor of 1Ω is connected with a battery.
➠ V = I × (R₂ + r)
➠ V = 1 × (5 + r) __ (ii)
By equating both equations, we get
⭆ 2 × (2 + r) = 1 × (5 + r)
⭆ 4 + 2r = 5 + r
⭆ 2r - r = 5 - 4
⭆ r = 1 Ω