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Calculate the reading of voltmeter V.

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Step 1: Calculate the reading of voltmeter V.
The voltmeter V is connected across the 1.2Ω1.2\Omega resistor. The total current from the ammeter, Itotal=2AI_{total} = 2A, flows through this resistor.
Using Ohm's Law, V=I×RV = I \times R.

V1=Itotal×RseriesV_1 = I_{total} \times R_{series} V1=2A×1.2ΩV_1 = 2A \times 1.2\Omega V1=2.4VV_1 = 2.4V

a) The reading of V is 2.4V\boxed{\text{2.4V}}.

Step 2: Calculate the total resistance of the parallel circuit.
The parallel circuit consists of 4Ω4\Omega, 1Ω1\Omega, and 2Ω2\Omega resistors.
The formula for equivalent resistance in parallel is:

1Rp=1R1+1R2+1R3\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} 1Rp=14Ω+11Ω+12Ω\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.

1Rp=14Ω+44Ω+24Ω\frac{1}{R_p} = \frac{1}{4\Omega} + \frac{4}{4\Omega} + \frac{2}{4\Omega} 1Rp=1+4+24Ω\frac{1}{R_p} = \frac{1+4+2}{4\Omega} 1Rp=74Ω\frac{1}{R_p} = \frac{7}{4\Omega} Rp=47ΩR_p = \frac{4}{7}\Omega Rp≈0.571ΩR_p \approx 0.571\Omega

b) The total resistance of the parallel circuit is 47Ω≈0.571Ω\boxed{\frac{4}{7}\Omega \approx \text{0.571}\Omega}.

Step 3: Find the current through the 2Ω2\Omega resistor.
First, calculate the voltage across the parallel combination. The total current Itotal=2AI_{total} = 2A flows through the equivalent parallel resistance Rp=47ΩR_p = \frac{4}{7}\Omega.

Vp=Itotal×RpV_p = I_{total} \times R_p Vp=2A×47ΩV_p = 2A \times \frac{4}{7}\Omega Vp=87VV_p = \frac{8}{7}V

Now, use Ohm's Law to find the current through the 2Ω2\Omega resistor, as the voltage across all parallel branches is the same (VpV_p).

I2Ω=VpR2ΩI_{2\Omega} = \frac{V_p}{R_{2\Omega}} I2Ω=87V2ΩI_{2\Omega} = \frac{\frac{8}{7}V}{2\Omega} I2Ω=814AI_{2\Omega} = \frac{8}{14}A I2Ω=47AI_{2\Omega} = \frac{4}{7}A I2Ω≈0.571AI_{2\Omega} \approx 0.571A

c) The current through the 2Ω2\Omega resistor is 47A≈0.571A\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.

Rtotal=Rseries+RpR_{total} = R_{series} + R_p Rtotal=1.2Ω+47ΩR_{total} = 1.2\Omega + \frac{4}{7}\Omega

Convert 1.2Ω1.2\Omega to a fraction: 1.2Ω=1210Ω=65Ω1.2\Omega = \frac{12}{10}\Omega = \frac{6}{5}\Omega.

Rtotal=65Ω+47ΩR_{total} = \frac{6}{5}\Omega + \frac{4}{7}\Omega

Find a common denominator, which is 35.

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