Let's solve the problem step-by-step.
### Step 1: Identify the Resistors and the Current
We have two resistors:
- [tex]\( R1 = 10 \ \Omega \)[/tex]
- [tex]\( R2 = 20 \ \Omega \)[/tex]
And a current of [tex]\( I_{\text{total}} = 0.1 \ \text{A} \)[/tex] passing through the lowest resistor, which is [tex]\( R1 \)[/tex].
### Step 2: Calculate the Equivalent Resistance of the Parallel Circuit
The formula for the equivalent resistance ([tex]\( R_{\text{parallel}} \)[/tex]) of two resistors in parallel is given by:
[tex]\[ \frac{1}{R_{\text{parallel}}} = \frac{1}{R1} + \frac{1}{R2} \][/tex]
So,
[tex]\[ \frac{1}{R_{\text{parallel}}} = \frac{1}{10} + \frac{1}{20} \][/tex]
Converting these to a common denominator, we get:
[tex]\[ \frac{1}{R_{\text{parallel}}} = \frac{2}{20} + \frac{1}{20} = \frac{3}{20} \][/tex]
Therefore,
[tex]\[ R_{\text{parallel}} = \frac{20}{3} \approx 6.67 \ \Omega \][/tex]
### Step 3: Calculate the Total Voltage Using Ohm's Law
Ohm's Law states that [tex]\( V = IR \)[/tex]. Applying this to find the total voltage across the network:
[tex]\[ V_{\text{total}} = I_{\text{total}} \times R_{\text{parallel}} \][/tex]
Substitute the values calculated:
[tex]\[ V_{\text{total}} = 0.1 \ \text{A} \times 6.67 \ \Omega \approx 0.67 \ \text{V} \][/tex]
### Step 4: Summarize the Results
We have determined:
- The equivalent resistance of the parallel combination ([tex]\( R_{\text{parallel}} \)[/tex]) is approximately [tex]\( 6.67 \ \Omega \)[/tex]
- The total voltage across the resistors ([tex]\( V_{\text{total}} \)[/tex]) is approximately [tex]\( 0.67 \ \text{V} \)[/tex]
- The total current passing through the circuit is [tex]\( I_{\text{total}} = 0.1 \ \text{A} \)[/tex]
Thus, the detailed solution for this question provides us with the following figures:
- Equivalent resistance: [tex]\( 6.67 \ \Omega \)[/tex]
- Total voltage: [tex]\( 0.67 \ \text{V} \)[/tex]
- Current passing through the lowest resistor: [tex]\( 0.1 \ \text{A} \)[/tex]
