The circuit shown in Fig. E $25.30$ contains two batteries, each with an emf and an internal resistance, and two resistors. Find the potential difference $V_{a c}$ of point $a$ with respect to point $c$ .

검증된 단계별 안내

Identify the components in the circuit: two batteries with emfs of 12.0 V and 5.0 V, internal resistances of 1.85 Ω and 1.25 Ω, and resistors of 8.50 Ω, 4.50 Ω, and 15.0 Ω.

Apply Kirchhoff's loop rule to the circuit. Choose a loop that includes points a and c, and write the equation for the sum of potential differences around the loop. Consider the direction of current flow and the polarity of the batteries.

Calculate the current in the circuit using the loop equation. You may need to solve a system of equations if there are multiple loops. Use Ohm's law, $ V = IR $, where $ V $ is the voltage, $ I $ is the current, and $ R $ is the resistance.

Determine the potential difference across each component between points a and c. For resistors, use $ V = IR $. For batteries, consider the emf and internal resistance.

Sum the potential differences from point a to point c to find $ V_{ac} $. Remember to account for the direction of current and the sign of each potential difference.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Kirchhoff's Loop Rule

Kirchhoff's Loop Rule states that the sum of the potential differences around any closed loop in a circuit must equal zero. This principle is based on the conservation of energy, ensuring that the energy supplied by the batteries is equal to the energy used by the resistors and any other components. Applying this rule helps determine unknown voltages or currents in complex circuits.

Electromotive Force (EMF) and Internal Resistance

Electromotive force (EMF) is the voltage generated by a battery or power source when no current flows. However, real batteries have internal resistance, which causes a voltage drop when current flows. The effective voltage across the battery terminals is the EMF minus the voltage drop due to internal resistance, affecting the total potential difference in the circuit.

Potential Difference

Potential difference, or voltage, between two points in a circuit is the work done to move a unit charge from one point to another. It is measured in volts and is crucial for understanding how energy is transferred in a circuit. Calculating the potential difference between points a and c involves considering the contributions from resistors and batteries along the path.