Consider the circuit shown in the figure, where the power...

Consider the circuit shown in the figure, where the power received by the resistor R is 14.0 W. 5.00 ? ?V 30.0 ? 40.0 ? R What are the possible values of R (in ?), if ?V = 75.0 V? smaller value R = ? larger value R = ?

Transcript

00:01 This question, what are the possible values of r if delta v is 75 volts? means if this battery is 75 volt, then what are the possible values of r? okay, it's already given that the power received by the resistor r is 14 watt.

00:22 Interesting.

00:24 So what we can do is first let's try to find the total current.

00:28 And for that we need to find effective resistance.

00:31 So effective resistance for this part.

00:33 Since this is in cs is going to be 40 plus r right so if we convert this into if we keep converting or condensing the circuit so this is equivalent resistance is going to be 40 plus r this is already 30 and this is already 5 and this is 75 then these two are in parallel right so its equivalent resistance is going to be we'll find it separately so this is 5 this is 75 its equivalent resistance r is going to be 30 times 40 plus r over 30 plus 40 plus r let's call it r e so that's going to be i think 1200 plus 30 r over 70 plus r that's going to be r and then r e and five is again in series so that's going to be a simple algebra edition right so that's just going to be 5 plus r e this is going to be 75 over here already all right so uh we can easily find a current now right the current is going to be current in the circuit is v over our effective so our effective is what 5 plus r e that is the current if that is the current then we need to find a current in this particular branch because after all we have to find the power for power we need the current right so for current in this branch we know that how to divide in the parallel circuits right if this is i then this is i1 the next the value of i1 is going to be i times the other resistance which is 30 over the sum of both resistances 30 plus and 40 plus r is the effective resistance over on the other side so that's 30 i over 70 plus r this is i 1 which is the current in the in the in the in the r resistance and we need to find the value of powers power is already 14 watt and power is what i.

02:41 Square r right now the power is i1 square times r and uh it means that i1 square times r is 14 now i one is what i 1 is 30 i over 70 plus r whole square times r is 14 and what is i i i is 70 i is this right so i will be 30 times 75 over 5 plus r effective over over 70 plus r whole square times r is 14...

Question

Consider the circuit shown in the figure, where the power received by the resistor R is 14.0 W. 5.00 ? ?V 30.0 ? 40.0 ? R What are the possible values of R (in ?), if ?V = 75.0 V? smaller value R = ? larger value R = ?

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