# voltage divider with multiple resistors

Discussion in 'General Electronics Discussion' started by stephan, Dec 13, 2013.

1. ### stephan

2
0
Dec 13, 2013
Hi,

I'm trying to build a book, with removable pages. When you remove a page I want to be able to detect that a page has been removed/ripped out and also which page has been removed. From my teacher, I have been given the advice of using a voltage divider (http://en.wikipedia.org/wiki/Voltage_divider) with multiple resistors. So it would look like the following:

The red lines are the pages, the black parts should be in the book's spine. When you rip out a page, this part of the circuit is not closed anymore and the resistor is not used.

I understand the general idea, although I don't understand how it works exactly. Most importantly, I don't understand how it would work for multiple resistors.

e.g. there is one example with 2 resistors (one is the "pull-up" and one the divider)

so, how would V_out be calculated for multiple resistors such as R2, R3, R4. I tried out the following formula, but building the circuit yielded different results for V_out. Additionally, I don't understand why the resistance of resistors that are put in parallel would be summed up, when determining the voltage of a certain point.

V_out = R_2 / (R_1 + R_2 + R_3 + R_4) * V_in

I'm looking for a formula how to calculate V_out for multiple resistors, so I can pick resistors yielding a close to uniform distribution for V_out

2. ### stephan

2
0
Dec 13, 2013
got it working, I also created a javascript script for it to calculate voltages for different resistor combinations

resistors = [
220,
560,
1000,
4700,
10000,
1000000,
10000000
];

voltage_in = 5;
pull_up = 1000;

function getVoltageOut(numberOfResistors, resistorsTakenOut) {
resistorsTakenOut = resistorsTakenOut || [];
var sum = pull_up;
for(var i=0; i<numberOfResistors; i++) {
if(resistorsTakenOut.indexOf(i) === -1) {
sum *= resistors;
}
};
return pull_up / sum * voltage_in;
}

var numberOfResistors = 4;
var getVoltageOutForResistors = getVoltageOut.bind(null, numberOfResistors);
var maxEncoding = Math.pow(2, 4);

for(var i = 0; i < maxEncoding; i++) {
var resistorsTakenOut = [];
var encoding = i;
var voltage;
var strEncoding = '';
//console.log('encoding '+encoding);

if(encoding%2 == 1) {
resistorsTakenOut.push(0);
strEncoding += '1';
} else {
strEncoding += '0';
}

encoding = Math.floor(encoding / 2);
if(encoding%2 == 1) {
resistorsTakenOut.push(1);
strEncoding = '1' + strEncoding;
} else {
strEncoding = '0' + strEncoding;
}

encoding = Math.floor(encoding / 2);
if(encoding%2 == 1) {
resistorsTakenOut.push(2);
strEncoding = '1' + strEncoding;
} else {
strEncoding = '0' + strEncoding;
}

encoding = Math.floor(encoding / 2);
if(encoding%2 == 1) {
resistorsTakenOut.push(3);
strEncoding = '1' + strEncoding;
} else {
strEncoding = '0' + strEncoding;
}

//console.log('strEncoding '+strEncoding);
voltage = getVoltageOutForResistors(resistorsTakenOut);
console.log(strEncoding+' : '+voltage+ ' V');
}

3. ### mursal

75
0
Dec 13, 2013
The page resistors are in parallel, so the overall resistance of the pages (Rpages) will increase when you pull a page out.

So, Rpages = 1/Rpages = 1/R1 + 1/R2 + 1/R3 + 1/Rn ........................
Where R1, R2, etc are page resistors and you can have as many pages as you like up to Rn

So for a given number of pages Vout = (Rpullup / Rpullup + Rpages) Vin

Hope this helps

Last edited: Dec 13, 2013