Consider the symbolic resistor network below

PHYSICS · Multi-part · A Level · Physics · Electricity · Electricity

Problem

Consider the symbolic resistor network below. All connecting wires are ideal, and the resistances are given in terms of

R

. • Resistors

R_{1}=R

and

R_{2}=2R

are connected in series to form Branch A. • Branch B consists of a single resistor

R_{3}=3R

. • Branches A and B are connected in parallel between terminals

M

and

N

. • A fourth resistor

R_{4}=R

is connected in series with the combination between

M

and

N

to form the complete network between terminals

S

and

T

as follows:

S

—

R_{4}

—

(\text{Branches A \& B in parallel})

—

T

. Answer the following. (1) Derive, in algebraic form, an expression for the equivalent resistance

R_{\text{eq}}

between terminals

S

and

T

in terms of

R

. Show all steps and simplify your result as much as possible. (2) Current

I_{0}

enters the network at terminal

S

. Express the current through resistor

R_{3}

in terms of

I_{0}

. Clearly outline your reasoning.