Electricity and Magnetism

20–134 Electricity and Magnetism

A pictorial representation

1

of this relation appears in Figure 20.2.

V

−

V

i

V

+

Potential

V

1

V

2

V

R

1

R

2

V

I

(12)

[→] I

(12)

[→]

FIGURE 20.2 The Potential Throughout the Battery–Two-Resistor Circuit

SAME The same current flows through each of the resistors,

I

1

= I

2

= I

(12)

,

and so we speak of the current, I

(12)

.

The constant of proportionality relating the potential difference across the pair to the unique

current through them is the effective resistance, R

(12)

.

V = I

(12)

R

(12)

.

Also,

V

1

= I

1

R

1

= I

(12)

R

1

and V

2

= I

2

R

2

= I

(12)

R

2

.

The energy constraint, V = V

1

+ V

2

, implies that

I

(12)

R

(12)

= I

(12)

R

1

+ I

(12)

R

2

= I

(12)



R

1

+ R

2



,

and thus

R

(12)

= R

1

+ R

2

.

The effectiv ...