Calculate the reading of voltmeter V.
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ScanSolve AI Answer
Step 1: Calculate the reading of voltmeter V.
The voltmeter V is connected across the $1.2\Omega$ resistor. The total current from the ammeter, $I_{total} = 2A$, flows through this resistor.
Using Ohm's Law, $V = I \times R$.
$$ V_1 = I_{total} \times R_{series} $$
$$ V_1 = 2A \times 1.2\Omega $$
$$ V_1 = 2.4V $$
a) The reading of V is $\boxed{\text{2.4V}}$.
Step 2: Calculate the total resistance of the parallel circuit.
The parallel circuit consists of $4\Omega$, $1\Omega$, and $2\Omega$ resistors.
The formula for equivalent resistance in parallel is:
$$ \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} $$
$$ \frac{1}{R_p} = \frac{1}{4\Omega} + \frac{1}{1\Omega} + \frac{1}{2\Omega} $$
To add these fractions, find a common denominator, which is 4.
$$ \frac{1}{R_p} = \frac{1}{4\Omega} + \frac{4}{4\Omega} + \frac{2}{4\Omega} $$
$$ \frac{1}{R_p} = \frac{1+4+2}{4\Omega} $$
$$ \frac{1}{R_p} = \frac{7}{4\Omega} $$
$$ R_p = \frac{4}{7}\Omega $$
$$ R_p \approx 0.571\Omega $$
b) The total resistance of the parallel circuit is $\boxed{\frac{4}{7}\Omega \approx \text{0.571}\Omega}$.
Step 3: Find the current through the $2\Omega$ resistor.
First, calculate the voltage across the parallel combination. The total current $I_{total} = 2A$ flows through the equivalent parallel resistance $R_p = \frac{4}{7}\Omega$.
$$ V_p = I_{total} \times R_p $$
$$ V_p = 2A \times \frac{4}{7}\Omega $$
$$ V_p = \frac{8}{7}V $$
Now, use Ohm's Law to find the current through the $2\Omega$ resistor, as the voltage across all parallel branches is the same ($V_p$).
$$ I_{2\Omega} = \frac{V_p}{R_{2\Omega}} $$
$$ I_{2\Omega} = \frac{\frac{8}{7}V}{2\Omega} $$
$$ I_{2\Omega} = \frac{8}{14}A $$
$$ I_{2\Omega} = \frac{4}{7}A $$
$$ I_{2\Omega} \approx 0.571A $$
c) The current through the $2\Omega$ resistor is $\boxed{\frac{4}{7}A \approx \text{0.571A}}$.
Step 4: Calculate the electromotive force (emf) of the cell.
First, calculate the total resistance of the entire circuit. This is the sum of the series resistor and the equivalent parallel resistance.
$$ R_{total} = R_{series} + R_p $$
$$ R_{total} = 1.2\Omega + \frac{4}{7}\Omega $$
Convert $1.2\Omega$ to a fraction: $1.2\Omega = \frac{12}{10}\Omega = \frac{6}{5}\Omega$.
$$ R_{total} = \frac{6}{5}\Omega + \frac{4}{7}\Omega $$
Find a common denominator, which is 35.
$$ R_{total} = \frac{6 \times 7}{
