Question

According to Ohm's Law, if you have a simple circuit (Figure 2), what happens to the voltage and current of the resistor as the resistance increases?

 If a 100 Ohm resistor is attached to a 5 V battery, how much current flows through the resistor? 

 If a wire's length is cut in half, what happens to the wire's resistance? 

 If a wire's area is reduced by half, what happens to the wire's resistance?

 If the diameter and length of a wire are split in half, what happens to the resistivity, p?

Answer 1

\(1 .\)

Write the expression for Ohm's Law:

\(V=I R\)

\(R=\frac{V}{I}\)

Here, \(R \propto V\) and \(R \propto \frac{1}{I}\)

Resistance is directly properly to the voltage. So, the voltage of the resistor increases as the resistance increases. Resistance is inversely properly to the current. So, the current of the resistor decreases as the resistance increases.

\(2 .\)

Consider the following data:

\(V=5 \mathrm{~V}\)

\(R=100 \Omega\)

Calculate the current flows through the resistor. \(I=\frac{V}{R}\)

\(=\frac{5}{100}\)

\(I=0.05 \mathrm{~A}\)

\(3 .\)

Consider the expression for resistance. \(R=\frac{\rho l}{A}\)

Here, the resistance is directly proportional to the length.

So, as the length is reduced by half, the resistance also reduced by half.

\(4 .\)

Consider the expression for resistance. \(R=\frac{\rho l}{A}\)

Here, the resistance is inversely proportional to the area.

So, as the area is reduced by half, the resistance becomes doubled.