A portable radio requires an emf of \(4.5 \mathrm{V}\). Olivia has only two non rechargeable \(1.5-\mathrm{V}\) batteries, but she finds a larger 6.0 -V battery. (a) How can she arrange the batteries to produce an emf of $4.5 \mathrm{V} ?$ Draw a circuit diagram. (b) Is it advisable to use this combination with her radio? Explain.

There are three batteries: 1. Two non-rechargeable 1.5 V batteries 2. One 6.0 V battery We need to find a way to arrange these batteries to produce an emf of 4.5 V.

When batteries are connected in series, their total emf is the sum of their individual emf values. If we connect one 1.5 V battery to another 1.5 V battery and then connect the resulting 3.0 V to the 6.0 V battery, we can achieve a total emf of 4.5 V. To accomplish this, the 6.0 V battery should be connected in an opposing direction to cancel out 1.5 V emf from the 3.0 V (1.5 + 1.5 V).

Draw a single loop circuit with the positive (+) terminal of 1.5 V batteries connected to the positive (+) terminal of the 6.0 V battery. Label the batteries as follows: B1 and B2 for the 1.5 V batteries and B3 for the 6.0 V battery. +---B1---B2---+ | | | | +-----B3------+

When batteries are connected in a way that their terminals are opposite, it can cause internal heating in the batteries, leading to reduced battery life and possibly damaging the radio. It is safest and best to use batteries designed for a specific emf, in this case, three 1.5 V batteries or one 4.5 V battery. In conclusion, (a) in order to achieve a 4.5 V emf, one 1.5 V battery should be connected in series with another 1.5 V battery, and the resulting 3.0 V should connect with the 6.0 V battery in an opposing direction. (b) However, using this combination of batteries is not advisable due to potential internal heating that can affect battery life and possibly damage the portable radio. The best option is to use batteries designed to provide the required emf.