A current source with emf 6 V and internal resistance 0.5 ohm is connected to a resistor. The current in the circuit is 4 A. Find the resistance of the resistor — Physics problems | PhysLabo
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Resistance of a resistor from the emf and the current

Medium 10 grade Electricity / Complete Electrical Circuit
Problem statement

A current source with emf $\varepsilon = 6$ V and internal resistance $r = 0.5$ ohm is connected to a resistor. The current in the circuit is $I = 4$ A. Find the resistance of the resistor.

Given
  • $\varepsilon = 6$ V
  • $r = 0.5$ ohm
  • $I = 4$ A
  • $R = ?$
Hints
Hint 1 / 2
First express the total resistance of the circuit: $R + r = \varepsilon/I$.
Hint 2 / 2
$\varepsilon/I$ gives the total resistance of the circuit; subtract the internal resistance from it.
Solution

From Ohm's law for a complete circuit $I = \varepsilon/(R + r)$ express the resistance of the resistor:

$$R = \frac{\varepsilon}{I} - r = \frac{6}{4} - 0.5 = 1.5 - 0.5 = 1 \text{ ohm}$$

Answer

$R = 1$ ohm

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