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The problem asks for the current in a battery that is connected to a combination of resistors. Here's a breakdown of the given information:

- The battery provides 18 V.
- There is a 3.0 Ω resistor connected in series.
- The series circuit is connected to a parallel arrangement of a 3.0 Ω resistor and a 6.0 Ω resistor.

To solve for the current, we can apply the following steps:

### 1. Calculate the equivalent resistance of the parallel resistors:
The two resistors (3.0 Ω and 6.0 Ω) are in parallel. The formula for the equivalent resistance \(R_{\text{eq}}\) of two resistors in parallel is:

\[
\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2}
\]

Substitute \(R_1 = 3.0 \, \Omega\) and \(R_2 = 6.0 \, \Omega\):

\[
\frac{1}{R_{\text{eq}}} = \frac{1}{3.0} + \frac{1}{6.0} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6}
\]

So,

\[
R_{\text{eq}} = \frac{6}{3} = 2.0 \, \Omega
\]

### 2. Calculate the total resistance:
Now that we have the equivalent resistance of the parallel combination as 2.0 Ω, we add it to the series resistor of 3.0 Ω:

\[
R_{\text{total}} = R_{\text{series}} + R_{\text{eq}} = 3.0 \, \Omega + 2.0 \, \Omega = 5.0 \, \Omega
\]

### 3. Use Ohm's Law to find the current:
The total voltage provided by the battery is 18 V. Using Ohm’s law:

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

Substitute \(V = 18 \, \text{V}\) and \(R_{\text{total}} = 5.0 \, \Omega\):

\[
I = \frac{18}{5.0} = 3.6 \, \text{A}
\]

Thus, the current in the battery is **3.6 A**.

### Final Answer:
The correct option is **A) 3.6 A**.

Would you like further details or have any questions?

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Here are 5 related questions:
1. How do you calculate the equivalent resistance of multiple resistors in parallel?
2. How does the total resistance change when resistors are connected in series versus parallel?
3. What is Ohm’s Law, and how is it applied to circuit problems?
4. How does increasing the resistance affect the current in a circuit?
5. What is the role of a battery in a circuit, and how does it influence current flow?

**Tip:** Always calculate equivalent resistances of parallel resistors before adding series resistors to avoid mistakes.

An 18 V battery and a 3.0 Ω resistor are connected in series with each other, and in series with a parallel arrangement of a 3.0 Ω resistor and a 6.0 Ω resistor. What is the current in the battery?

Learn how to calculate the current in a battery connected in series and parallel with resistors. This example uses Ohm's Law and the formula for equivalent resistance of parallel resistors. Suitable for Grades 9-12.

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