15. Direct Current

D.C. Circuits Resistors in Series Rtotal = R1 + R2 + R3 Resistors in Parallel 321total R 1 R 1 R 1 R 1  Potential Divider Principle Two resistors are connected in series with a source of e.m.f. V1= ( R1 R1+R2 ) E V2= ( R2 R1+R2 ) E Another type of potential divider is a potentiometer. A potentiometer used as a potential divider A variable direct voltage may be obtained from a fixed supply voltage. Moving the sliding contact from A to B in the circuit shown above increases the output from zero to E. Light Dependent Resistor (LDR) A LDR is a resistor whose resistance decreases as light intensity falling on it increases. (Light falling on the LDR releases more charge carriers to conduct current.) A thermistor (or thermally sensitive resistor) is a resistor whose resistance R t changes greatly with temperature. Thermistor Commonly used thermistors have a negative temperature coefficient, i.e. resistance Rt decreases as temperature increases. E B A Variable output voltage

Electromotive force (e.m.f.), E, is the amount of energy transferred per unit charge from some other form of energy into electrical energy when charge is moved round a complete circuit. E = 𝑊 𝑄 Internal Resistance and Terminal potential diference As shown in the diagram below, internal resistance is normally denoted as r and in a circuit it is denoted as a resistor that is in series with the source, and directly connected to the negative terminal. R is normally the external resistance (the load that is connected to the source, which is indicated by the dotted line circle.) While E is the e.m.f. of the source. e.m.f. = p.d. across internal resistor + p.d. across external resistor 𝐸 = 𝑣 + 𝑉 𝐸 = 𝐼𝑟 + 𝐼𝑅 𝐼𝑅 = 𝐸 − 𝐼𝑟 The quantity of ( E – Ir) therefore indicates the amount of voltage that reaches the external components of a circuit and is known as the terminal p.d. E r R I The source

Perspective of power Power generated by source = Sum of power dissipated in other components. Hence, in the similar circuit, 𝑃𝑠𝑜𝑢𝑟𝑐𝑒 = 𝑝 + 𝑃 𝐼𝐸 = 𝐼𝑣 + 𝐼𝑉 = 𝐼2𝑟 + 𝐼2𝑅 where: p is the power dissipated due to internal resistance and P is the power dissipated due to external load. v is the potential difference across r and V is the potential difference across R. Use of Potentiometer as a means of comparing potential differences E r R I

If the wire is of uniform cross -sectional area and resistivity, the potential gradient k (“potential difference per unit length”) along the wire is uniform and given by: XY XY l Vk  where lXY : length of slide wire The potential difference, VXJ across a certain length l of the wire is directly proportional to the length l, i.e., VXJ = klXJ To find the value of VAB : Since VAB = VXJ = klXJ and XY XY l Vk  , ll VV XJ XY XY AB  𝑉𝐴𝐵 = (𝑙𝑋𝐽 𝑙𝑋𝑌 ) 𝑉𝑋𝑌 where VXY = E if the driver cell has no internal resistance.