# 4.14: Tortures for the Brain

I don’t know if any of the examples in this section have any practical applications, but they are excellent ways for torturing students, or for whiling away rainy Sunday afternoons.

### Q4.14.1

The drawing shows 12 resistances, each of value r \(\Omega\), arranged along the edges of a cube. What is the resistance across opposite corners of the cube?

### Q4.14.2

The drawing shows six resistors, each of resistance 1 \(\Omega\), arranged along the edges of a tetrahedron. A 12 V battery is connected across one of the resistors. Calculate the current between points A and B.

### Q4.14.3

The figure shows six resistors, whose resistances in ohms are marked, arranged along the edges of a tetrahedron. Calculate the net resistance between C and D.

### Q4.14.4

R_{1} = 8 \(\Omega\) and R_{2} = 0.5 \(\Omega\) are connected across a battery. The rate at which heat is generated is the same whether they are connected in series or in parallel. What is the internal resistance r of the battery?

### Q4.14.5

R_{1} = 0.25 \(\Omega\) and R_{2} = ? are connected across a battery whose internal resistance r is 0.5 \(\Omega\). The rate at which heat is generated is the same whether they are connected in series or in parallel. What is the value of R_{2}?

### Q4.14.6

In the above circuit, each resistance is 1 ohm. What is the net resistance between A and B if the chain is of infinite length?

### Q4.14.7

What is the resistance between A and B in question 4.14.6 if the chain is not of infinite length, but has n “links” – i.e. 2n resistors in all?

### Q4.14.8

In the circuit below, what is the potential difference between A and B, and what is the current in each resistor?