The potential difference between the terminals of a battery of emf 6.0 V and internal resistance 1 Ω drops to 5.8 V when connected across an external resistor. Find the resistance of the external resistor.
The emf of the cell, E=6V
The value of internal resistance, r= 1 Ω
The volt meter reading across the setup, V=5.8V
The value of external resistance= R Ω
Figure shows the overview of the setup.
The voltage across the cell will be equal to that across the external resistance. So,
The current flowing through the internal and external resistance are the same.
By substituting the given values in the eqn.1, we get i as
This current also circulate through the external resistance R. Hence from the eqn.1, we can write its expression as,
By substituting the values of ‘i’ and V, we get
Hence the resistance of the external resistor is 29Ω.
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