A voltage of 20 V is required to cause a current of 2 A to flow in a resistor of resistance $$ 10 \Omega $$. What voltage would be required to make the same current flow if the resistance were $$ 40 \Omega $$? [80V]

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1. The relationship between voltage, current, and resistance is given by Ohm's Law:  
   $$
   V = IR
   $$

2. For the resistor with $$ R = 10 \, \Omega $$, the voltage required to produce a current of $$ I = 2 \, \text{A} $$ is:  
   $$
   V = (2 \, \text{A}) \times (10 \, \Omega) = 20 \, \text{V}
   $$

3. When the resistance is increased to $$ R = 40 \, \Omega $$, and the same current of $$ 2 \, \text{A} $$ is required, the new voltage is:  
   $$
   V = (2 \, \text{A}) \times (40 \, \Omega) = 80 \, \text{V}
   $$

4. Therefore, the voltage required to make the current of $$ 2 \, \text{A} $$ flow through a $$ 40 \, \Omega $$ resistor is $$ 80 \, \text{V} $$.
To find the voltage needed for a 2 A current through a 40 Ω resistor, use Ohm's Law: $$ V = IR $$. So, $$ V = 2 \, \text{A} \times 40 \, \Omega = 80 \, \text{V} $$.

A voltage of 20 V is required to cause a current of 2 A to flow in a resistor of resistance \( 10 \Omega \). What voltage would be required to make the same current flow if the resistance were \( 40 \Omega \)? [80V]

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