Absolutely, let's tackle this problem step-by-step.
### Given:
1. Internal resistance of the battery, [tex]\( R_{\text{battery}} = 1 \, \Omega \)[/tex]
2. External resistance [tex]\( R_{\text{external}} = 12 \, \Omega \)[/tex]
3. Voltage of the battery [tex]\( V_{\text{battery}} = 10 \, \text{V} \)[/tex]
### Steps to Solve:
1. Calculate the Total Resistance:
The total resistance in the circuit is the sum of the internal resistance of the battery and the external resistance.
[tex]\[
R_{\text{total}} = R_{\text{battery}} + R_{\text{external}}
\][/tex]
Substitution of values gives:
[tex]\[
R_{\text{total}} = 1 \, \Omega + 12 \, \Omega = 13 \, \Omega
\][/tex]
2. Calculate the Current Through the Circuit:
Using Ohm's Law, the current [tex]\( I \)[/tex] through the circuit can be calculated using the formula:
[tex]\[
I = \frac{V_{\text{battery}}}{R_{\text{total}}}
\][/tex]
Substitute the given values:
[tex]\[
I = \frac{10 \, \text{V}}{13 \, \Omega} \approx 0.7692 \, \text{A}
\][/tex]
3. Interpret the Result:
The total current through the circuit is approximately [tex]\( 0.769 \, \text{A} \)[/tex].
So, the total resistance in the circuit is [tex]\( 13 \, \Omega \)[/tex] and the current through the circuit is approximately [tex]\( 0.7692 \, \text{A} \)[/tex].
