A battery of four 1.5 V cells in series powers a circuit with two 200 ohm resistors in parallel, connected to…

Question

A battery of four 1.5 V cells in series powers a circuit with two 200 ohm resistors in parallel, connected to a 400 ohm resistor in series. What is the voltmeter reading across the 400 ohm resistor?

ScanSolve AI Tutor · Accepted Answer

To calculate the reading on the voltmeter, we need to find the voltage across the $400 \, \Omega$ resistor. This requires determining the total voltage of the battery and the total current flowing through the circuit.

Assumption: The battery consists of four cells connected in series. Assuming each cell provides $1.5 \, \text{V}$ , the total voltage of the battery is $4 \times 1.5 \, \text{V} = 6 \, \text{V}$ .

Calculate the equivalent resistance of the two $200 \, \Omega$ resistors connected in parallel.
$\frac{1}{R_{p}} = \frac{1}{200 \, \Omega} + \frac{1}{200 \, \Omega}$ $\frac{1}{R_{p}} = \frac{2}{200 \, \Omega}$ $R_{p} = \frac{200 \, \Omega}{2} = 100 \, \Omega$
Calculate the total equivalent resistance of the entire circuit.
The parallel combination ( $R_p$ ) is in series with the $400 \, \Omega$ resistor.
$R_{total} = R_p + 400 \, \Omega$ $R_{total} = 100 \, \Omega + 400 \, \Omega = 500 \, \Omega$
Calculate the total current flowing from the battery.
Using Ohm's Law, $I = \frac{V}{R}$ .
$I_{total} = \frac{V_{total}}{R_{total}}$ $I_{total} = \frac{6 \, \text{V}}{500 \, \Omega}$ $I_{total} = 0.012 \, \text{A}$
Calculate the voltage drop across the $400 \, \Omega$ resistor.
Since the $400 \, \Omega$ resistor is in series with the parallel combination, the total current $I_{total}$ flows through it. The voltmeter measures this voltage.
$V_{400} = I_{total} \times 400 \, \Omega$ $V_{400} = 0.012 \, \text{A} \times 400 \, \Omega$ $V_{400} = 4.8 \, \text{V}$
The reading on the voltmeter is $\text{4.8 V}$ .

A battery of four 1.5 V cells in series powers a circuit with two 200 ohm resistors in parallel, connected to a 400 ohm resistor in series. What is the voltmeter reading across the 400 ohm resistor?

Answer

Step-by-step solution

Calculate the equivalent resistance of the two $200 \, \Omega$ resistors connected in parallel.

Calculate the total equivalent resistance of the entire circuit.

Calculate the total current flowing from the battery.

Calculate the voltage drop across the $400 \, \Omega$ resistor.

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More Physics Questions

A battery of four 1.5 V cells in series powers a circuit with two 200 ohm resistors in parallel, connected to a 400 ohm resistor in series. What is the voltmeter reading across the 400 ohm resistor?

Answer

Step-by-step solution

Calculate the equivalent resistance of the two 200 Ω200 \, \Omega200Ω resistors connected in parallel.

Calculate the total equivalent resistance of the entire circuit.

Calculate the total current flowing from the battery.

Calculate the voltage drop across the 400 Ω400 \, \Omega400Ω resistor.

Try one yourself

Still stuck on this one?

More Physics Questions

Calculate the equivalent resistance of the two $200 \, \Omega$ resistors connected in parallel.

Calculate the voltage drop across the $400 \, \Omega$ resistor.