Questions: Problem 13.00 E 6 - DEPENDENT MULTI-PART PROBLEM - ASSIGN ALL PARTS. Four 22-Ω resistors are connected in series to a 18-V battery of negligible internal resistance. Part 2 of 2 Problem 13.00E6.b - Calculating the voltage difference across each resistor Determine the voltage difference across each resistor.

Solution Steps

In a series circuit, the total resistance is the sum of the individual resistances. Here, we have four resistors, each with a resistance of \(22 \, \Omega\). Therefore, the total resistance \(R_{\text{total}}\) is:

\[ R_{\text{total}} = 4 \times 22 \, \Omega = 88 \, \Omega \]

Using Ohm's Law, the total current \(I\) flowing through the circuit can be calculated using the formula:

\[ I = \frac{V_{\text{total}}}{R_{\text{total}}} \]

where \(V_{\text{total}} = 18 \, \text{V}\) is the voltage of the battery. Substituting the values, we get:

\[ I = \frac{18 \, \text{V}}{88 \, \Omega} \approx 0.2045 \, \text{A} \]

In a series circuit, the current through each resistor is the same. The voltage difference \(V\) across each resistor can be calculated using Ohm's Law:

\[ V = I \times R \]

For each \(22 \, \Omega\) resistor, the voltage difference is:

\[ V = 0.2045 \, \text{A} \times 22 \, \Omega \approx 4.499 \, \text{V} \]

Final Answer