checkpoint_09

Electric Current

Two Resistors

Two cylindrical resistors are made from the same material and are equal in length. The first resistor has diameter [d], and the second resistor has diameter [2 d].

1)

If the same current flows through both, compare the voltage across the two resistors:

• [V_1 > V_2]

2)

Two cylindrical resistors are made from the same material and are equal in diameter. The first resistor has length [L], and the second resistor has length [2 L].

If the same current flows through both, compare the voltage across the two resistors:

• [V_1 < V_2]

Resistor Network

Three resistors are connected to a battery with emf [V] as shown. The resistances of the resistors are all the same, i.e. [R_1 = R2 = R3 = R].

1)

Compare the current through R2 with the current through R3:

• [I_2 = I_3]

2)

Compare the current through R1 with the current through R2:

• [\frac{ I_1}{ I_2} = 2]

3)

Compare the current through R1 with the current through R2:

• [V_2 = V_3 < V]

4)

Compare the the voltage across R1 with the voltage across R2.

• [ V_1 = 2 V_2 = V]

Current Density

The SAME amount of current [I] passes through three different resistors. [R_2] has twice the cross-sectional area and the same length as [R_1], and [R_3] is three times as long as [R_1] but has the same cross-sectional area as [R_1].

current_density.png

In which case is the CURRENT DENSITY through the resistor the smallest?

• Case 2