Internal ResistanceReal batteries have a small internal resistance, r, which is small but non-zero

Terminal voltage: V Vb Va

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I r(In reality, due to r, even if you short the leads you don’t get infinite current). In this course, when internal resistance or terminal voltage is not mentioned, we typically don’t need to consider the battery’s internal resistance

Kirchhoff’s Loop Rules

are important for complicated circuits. Especially when there is more than 1 battery.

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Kirchhoff’s Rules1. Sum of currents entering any junction in a circuit

must equal sum of currents leaving that junction.

I1 I2 I3

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V E ds 0Close path

Kirchhoff’s Rules2. Sum of potential differences across all

elements around any closed circuit loop must be zero. �

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Steps of Solving Circuit Problem

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1. Straighten out circuit (make squares)

2. Simplify resistors in series/parallel

3. Assign current loops (arbitrary)

4. Write loop equations (1 per loop)

5. Solve

Example: Simple CircuitYou can simplify resistors in series (but don’t need to)

What is current through the bottom battery?

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Example: Simple CircuitStart at a in both loops

Walk in direction of current

2 I1R I1 I2 R 0

I2 I1 R 02 I1R 0 I1

R

Add these:

I2 I1 R I 2

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I1R

I2 0

We wanted I2:

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Group Problem: CircuitFind meters’ values. All resistors are R, batteries are

HARDER EASIER

Voltage MeterA ideal Voltage meter can be considered to have a infinite resistance.

When we use it to measure the voltage between two point, it does not let current flow through it and doesn’t changed the voltage between those two points.

The current through a Voltage meter is ZERO.

Ampere MeterA ideal Ampere meter can be considered to have zero resistance.

When we use it to measure the current along any path, it doesn’t need any voltage drop though the Ampere meter, and doesn’t change the current in that path.

The Voltage difference across an Ampere meter is ZERO.

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Group Problem: CircuitFind meters’ values. All resistors are R, batteries are

HARDER EASIER

PRS Questions: More Light Bulbs

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